Sequences on ACT Math Strategy Guide and Review

Sequences on ACT Math Strategy Guide and Review SAT / ACT Prep Online Guides and Tips Sequences are patterns of numbers that follow a particular set of rules. Whether new term in the sequence is found by an arithmetic constant or found by a ratio, each new number is found by a certain rule- the same rule- each time. There are several different ways to find the answers to the typical sequence questions- †What is the first term of the sequence?†, â€Å"What is the last term?†, â€Å"What is the sum of all the terms?†- and each has its benefits and drawbacks. We will go through each method, and the pros and cons of each, to help you find the right balance between memorization, longhand work, and time strategies. This will be your complete guide to ACT sequence problems- the various types of sequences there are, the typical sequence questions you’ll see on the ACT, and the best ways to solve these types of problems for your particular ACT test taking strategies. Before We Begin Take note that sequence problems are rare on the ACT, never appearing more than once per test. In fact, sequence questions do not even appear on every ACT, but instead show up approximately once every second or third test. What does this mean for you? Because you may not see a sequence at all when you go to take your test, make sure you prioritize your ACT math study time accordingly and save this guide for later studying. Only once you feel you have a solid handle on the more common types of math topics on the test- triangles (comng soon!), integers, ratios, angles, and slopes- should you turn your attention to the less common ACT math topics like sequences. Now let's talk definitions. What Are Sequences? For the purposes of the ACT, you will deal with two different types of sequences- arithmetic and geometric. An arithmetic sequence is a sequence in which each term is found by adding or subtracting the same value. The difference between each term- found by subtracting any two pairs of neighboring terms- is called $d$, the common difference. -5, -1, 3, 7, 11, 15†¦ is an arithmetic sequence with a common difference of 4. We can find the $d$ by subtracting any two pairs of numbers in the sequence- it doesn’t matter which pair we choose, so long as the numbers are next to one another. $-1 - -5 = 4$ $3 - -1 = 4$ $7 - 3 = 4$ And so on. 12.75, 9.5, 6.25, 3, -0.25... is an arithmetic sequence in which the common difference is -3.25. We can find this $d$ by again subtracting pairs of numbers in the sequence. $9.5 - 12.75 = -3.25$ $6.25 - 9.5 = -3.25$ And so on. A geometric sequence is a sequence of numbers in which each successive term is found by multiplying or dividing by the same amount each time. The difference between each term- found by dividing any neighboring pair of terms- is called $r$, the common ratio. 212, -106, 53, -26.5, 13.25†¦ is a geometric sequence in which the common ratio is $-{1/2}$. We can find the $r$ by dividing any pair of numbers in the sequence, so long as they are next to one another. ${-106}/212 = -{1/2}$ $53/{-106} = -{1/2}$ ${-26.5}/53 = -{1/2}$ And so on. Though sequence formulas are useful, they are not strictly necessary. Let's look at why. Sequence Formulas Because sequences are so regular, there are a few formulas we can use to find various pieces of them, such as the first term, the nth term, or the sum of all our terms. Do take note that there are pros and cons for memorizing formulas. Pros- formulas are a quick way to find your answers, without having to write out the full sequence by hand or spend your limited test-taking time tallying your numbers. Cons- it can be easy to remember a formula incorrectly, which would lead you to a wrong answer. It also is an expense of brainpower to memorize formulas that you may or may not even need come test day. If you are someone who prefers to use and memorize formulas, definitely go ahead and learn these! But if are not, then you are still in luck; most (though not all) ACT sequence problems can be solved longhand. So if you have the patience- and the time to spare- then don’t worry about memorizing formulas. That all being said, let’s take a look at our formulas so that those of you who want to memorize them can do so and so that those of you who don’t can still understand how they work. Arithmetic Sequence Formulas $$a_n = a_1 + (n - 1)d$$ $$\Sum \terms = (n/2)(a_1 + a_n)$$ These are our two important arithmetic sequence formulas and we will go through how each one works and when to use them. Terms Formula $a_n = a_1 + (n - 1)d$ If you need to find any individual piece of your arithmetic sequence, you can use this formula. First, let us talk about why it works and then we can look at some problems in action. $a_1$ is the first term in our sequence. Though the sequence can go on infinitely, we will always have a starting point at our first term. $a_n$ represents any missing term we want to isolate. For instance, this could be the 4th term, the 58th, or the 202nd. Why does this formula work? Well let’s say we wanted to find the 2nd term in the sequence. We find each new term by adding our common difference, or $d$, so the second term would be: $a_2 = a_1 + d$ And we would then find the 3rd term in the sequence by adding another $d$ to our existing $a_2$. So our 3rd term would be: $a_3 = (a_1 + d) + d$ Or, in other words: $a_3 = a_1 + 2d$ And the 4th term of the sequence, found by adding another $d$ to our existing third term, would continue this pattern: $a_4 = (a_1 + 2d) + d$ Or $a_4 = a_1 + 3d$ So, as you can see, each term in the sequence is found by adding the first term to $d$, multiplied by $n - 1$. (The 3rd term is $2d$, the 4th term is $3d$, etc.) So now that we know why the formula works, let’s look at it in action. What is the difference between each term in an arithmetic sequence, if the first term of the sequence is -6 and the 12th term is 126? 3 4 6 10 12 Now, there are two ways to solve this problem- using the formula, or finding the difference and dividing by the number of terms between each number. Let’s look at both methods. Method 1: Arithmetic Sequence Formula If we use our formula for arithmetic sequences, we can find our $d$. So let us simply plug in our numbers for $a_1$ and $a_n$. $a_n = a_1 + (n - 1)d$ $126 = -6 + (12 - 1)d$ $126 = -6 + 11d$ $132 = 11d$ $d = 12$ Our final answer is E, 12. Method 2: finding difference and dividing Because the difference between each term is regular, we can find that difference by finding the difference between our terms and then dividing by the number of terms in between them. Note: be very careful when you do this! Though we are trying to find the 12th term, there are NOT 12 terms between the first term and the 12th- there are actually 11. Why? Let’s look at a smaller scale sequence of 3 terms. 4, __, 8 If you wanted to find the difference between these terms, you would again find the difference between 4 and 8 and divide by the number of terms separating them. You can see that there are 3 total terms, but 2 terms separating 4 and 8. 1st: 4 to __ 2nd: __ to 8 When given $n$ terms, there will always be $n - 1$ terms between the first number and the last. So, if we turn back to our problem, now we know that our first term is -6 and our 12th is 126. That is a difference of: $126 - -6$ $126 + 6$ $132$ And we must divide this number by the number of terms between them, which in this case is 11. $132/11$ $12$ Again, the difference between each number is E, 12. As you can see, the second method is just another way of using the formula without actually having to memorize the formula. How you solve these types of questions completely depends on how you like to work and your own personal ACT math strategies. Sum Formula $\Sum \terms = (n/2)(a_1 + a_n)$ This formula tells us the sum of the terms in an arithmetic sequence, from the first term ($a_1$) to the nth term ($a_n$). Basically, we are multiplying the number of terms, $n$, by the average of the first term and the nth term. Why does this work? Well let’s look at an arithmetic sequence in action: 4, 7, 10, 13, 16, 19 This is an arithmetic sequence with a common difference, $d$, of 3. A neat trick you can do with any arithmetic sequence is to take the sum of the pairs of terms, starting from the outsides in. Each pair will have the same exact sum. So you can see that the sum of the sequence is $23 * 3 = 69$. In other words, we are taking the sum of our first term and our nth term (in this case, 19 is our 6th term) and multiplying it by half of $n$ (in this case $6/2 = 3$). Another way to think of it is to take the average of our first and nth terms- ${4 + 19}/2 = 11.5$ and then multiply that value by the number of terms in the sequence- $11.5 * 6 = 69$. Either way, you are using the same basic formula, so it just depends on how you like to think of it. Whether you prefer $(n/2)(a_1 + a_n)$ or $n({a_1 + a_n}/2)$ is completely up to you. Now let’s look at the formula in action. Andrea is selling boxes of cookies door-to-door. On her first day, she sells 12 boxes of cookies, and she intends to sell 5 more boxes per day than on the day previous. If she meets her goal and sells boxes of cookies for a total of 10 days, how many boxes total did she sell? 314 345 415 474 505 As with almost all sequence questions on the ACT, we have the choice to use our formulas or do the problem longhand. Let’s try both ways. Method 1: formulas We know that our formula for arithmetic sequence sums is: $\Sum = (n/2)(a_1 + a_n)$ In order to plug in our necessary numbers, we must find the value of our $a_n$. Once again, we can do this via our first formula, or we can find it by hand. As we are already using formulas, let us use our first formula. $a_n = a_1 + (n - 1)d$ We are told that the first term in our sequence is 12. We also know that she sells cookies for 10 days and that, each day, she sells 5 more boxes of cookies. This means we have all our pieces to complete this formula. $a_n = 12 + (10 - 1)5$ $a_10 = 12 + (9)5$ $a_10 = 12 + 45$ $a_10 = 57$ Now that we have our value for $a_n$ (in this case $a_10$), we can complete our sum formula. $(n/2)(a_1 + a_n)$ $(10/2)(12 + 57)$ $5(69)$ $345$ Our final answer is B, 345. Method 2: longhand Alternatively, we can solve this problem by doing it longhand. It will take a little longer, but this way also carries less risk of mis-remembering a formula. The decision is, as always, completely up to you on how you choose to solve these kinds of questions. First, let us write out our sequence, beginning with 12 and adding 5 to each subsequence number, until we find our nth (10th) term. 12, 17, 22, 27, 32, 37, 42, 47, 52, 57 Now, we can either add them up all by hand- $12 + 17 + 22 + 27 + 32 + 37 + 42 + 47 + 52 + 57 = 345$ Or we can use our arithmetic sequence sum trick and divide the sequence into pairs. We can see that there are 5 pairs of 69, so $5 * 69 = 345$. Again, our final answer is B, 345. Whoo! Only one more formula to go! Geometric Sequence Formulas $$a_n = a_1( r^{n - 1})$$ (Note: there is a formula to find the sum of a geometric sequence, but you will never be asked to find this on the ACT, and so it is not included in this guide.) This formula, as with the first arithmetic sequence formula, will help you find any number of missing pieces in your sequence. Given two pieces of information about your sequence ($a_n$ $a_1$, $a_1$ $r$, or $a_n$ $r$), you can find the third. And, as always with sequences, you have the choice of whether to solve your problem longhand or with a formula. What is the first term in a geometric sequence if each number is found by multiplying the previous term by -3 and the 8th term is 4,374? -0.222 0.667 -2 6 -18 Method 1: formula If you’re one for memorizing formulas, we can simply plug in our values into our equation in place of $a_n$, $n$, and $r$ in order to solve for $a_1$. $a_n = a_1( r^{n - 1})$ $4374 = a_1(-3^{8 - 1})$ $4374 = a_1(-3^7)$ $4374 = a_1(-2187)$ $-2 = a_1$ So our first term in the sequence is -2. Our final answer is C, -2. Method 2: longhand Alternatively, as always, we can take a little longer and solve them problem by hand. First, set out our number of terms in order to keep track of them, with our 8th term, 4374, last. ___, ___, ___, ___, ___, ___, ___, 4374 Now, let’s divide each number by -3 down the sequence until we reach the beginning. ___, ___, ___, ___, ___, ___, -1458, 4374 ___, ___, ___, ___, ___, 486, -1458, 4374 And, if we keep going thusly, we will eventually get: -2, 6, -18, 54, -162, 486, -1458, 4374 Which means that we can see that our first term is -2. Again, our final answer is C, -2. As with all sequence solving methods, there are benefits and drawbacks to solving the question in each way. If you choose to use formulas, make very sure you can remember them exactly. And if you solve the questions by hand, be very careful to find the exact number of terms in the sequence. The ACT will always provide bait answers for anyone who is one or two terms off the nth term- in this problem, if you had accidentally assigned 4374 as the 7th term or the 9th term, you would have chosen answer B or D. Once you find the strategy that works best for you, the pieces will all fall into place. Typical ACT Sequences Questions Because all sequence questions on the ACT can be solved (if sometimes arduously) without the use or knowledge of sequence formulas, the test-makers will only ever ask you for a limited number of terms or the sum of a small number of terms (usually less than 12). As we saw above, you may be asked to find the 1st term in a sequence, the nth term, the difference between your terms (whether a common difference, $d$, or a common ratio, $r$), or the sum of your terms in arithmetic sequences only. You also may be asked to find an unusual twist on a sequence question that combines your knowledge of sequences. For example: What is the sum of the first 5 terms of an arithmetic sequence in which the 6th term is 14 and the 11th term is 22? 2.2 6.0 12.4 32.6 46.0 Again, let us look at both formulaic and longhand methods for how to solve a problem like this. Method 1: formulas In order to find our common difference, we can use our main arithmetic sequence formula. But this time, instead of beginning with the actual $a_1$, we are beginning with our 6th term, as this is what we are given. Essentially, we are designating our 6th term as our 1st term and our 11th term as our 6th term and then plugging these values into our formula. $a_n = a_1 + (n - 1)d$ $22 = 14 + (6 - 1)d$ $22 = 14 + 5d$ $8 = 5d$ $1.6 = d$ Now, we can find our actual 1st term by using the $d$ we just found and our 11th term value of 22. $a_n = a_1 + (n - 1)d$ $22 = a_1 + (11 - 1)1.6$ $22 = a_1 + (10)1.6$ $22 = a_1 + 16$ $6 = a_1$ The 1st term of our sequence is 6. Now, we need to find the 5th term of our sequence in order to use our arithmetic sequence sum formula to find the sum of the first 5 terms. $a_n = a_1 + (n - 1)d$ $a_5 = 6 + (5 - 1)1.6$ $a_5 = 6 + (4)1.6$ $a_5 = 6 + 6.4$ $a_5 = 12.4$ And finally, we can find the sum of our first 5 terms by using our sum formula and plugging in the values we found. $(n/2)(a_1 + a_n)$ $5/2(6 + 12.4)$ $2.5(18.4)$ $46$ Our final answer is E, 46. As you can see, this problem still took a significant amount of time using our formulas because there were so many moving pieces. Let us look at this problem were we to solve it longhand instead. Method 2: longhand First, let us find our common difference by finding the difference between our 6th term and our 11th term and dividing by how many terms are in between them, which in this case is 5. (Why 5? There is one term between the 6th and 7th terms, another between the 7th and 8th, another between the 8th and 9th, another between the 9th and 10th, and the last between the 10th and 11th terms. This makes a total of 5 terms.) This gives us: $22 - 14 = 8$ $8/5 = 1.6$ Now, let us simply find all the numbers in our sequence by working backwards and subtracting 1.6 from each term. ___, ___, ___, ___, ___, 14, ___, ___, ___, ___, 22 ___, ___, ___, ___, ___, 14, ___, ___, ___, 20.4, 22 ___, ___, ___, ___, ___, 14, ___, ___, 18.8, 20.4, 22 And so on, until all the spaces are filled. 6, 7.6, 9.2, 10.8, 12.4, 14, 15. 6, 17.2, 18.8, 20.4, 22 Now, simply add up the first 5 terms. $6 + 7.6 + 9.2 + 10.8 + 12.4$ $46$ Our final answer is E, 46. Again, you always have the choice to use formulas or longhand to solve these questions and how you prioritize your time (and/or how careful you are with your calculations) will ultimately decide which method you use. You've seen the typical ACT sequence questions, so let's talk strategies. Tips For Solving Sequence Questions Sequence questions can be somewhat tricky and arduous to slog through, so keep in mind these ACT math tips on sequences as you go through your studies: 1: Decide before test day whether or not you will use the sequence formulas Before you go through the effort of committing your formulas to memory, think about the kind of test-taker you are. If you are someone who lives and breathes formulas, then go ahead and memorize them now. Most sequence questions (though, as we saw above, not all of them) will go much faster once you have the formulas down straight. If, however, you would rather dedicate your time and brainpower to other math topics or to the method of performing sequence questions longhand, then don’t worry about your formulas! Don’t even bother to try to remember them- just decide here and now not to use them and forget about the formulas entirely. Unless you can be sure to remember them correctly, a formula will hinder more than help you when it comes time to take your ACT, so make the decision now to either memorize them or forget about them. 2: Write your values down and keep your work organized Though many calculators can perform long strings of calculations, sequence questions by definition involve many different values and terms. Small errors in your work can cause a cascade effect. One mistyped digit in your calculator can throw off your work completely, and you won’t know where the error happened if you do not keep track of your values. Always remember to write down your values and label them in order to prevent a misstep somewhere down the line. 3: Keep careful track of your timing No matter how you solve a sequence question, these types of problems will generally take you more time than other math questions on the ACT. For this reason, most all sequence questions are located in the last third of the ACT math section, which means the test-makers think of sequences as a â€Å"high difficulty† level problem. Time is your most valuable asset on the ACT, so always make sure you are using yours wisely. If you can answer two other math questions in the time it takes you to answer one sequence question, then maximize your point gain by focusing on the other two questions. Always remember that each question on the ACT math section is worth the same amount of points, so prioritize quantity and don’t let your time run out trying to solve one problem. If you feel that you can answer a sequence problem quickly, go ahead! But if you feel it will take up too much time, move on and come back to it later. Ready to put your knowledge to the test? Test Your Knowledge Now let’s test your sequence knowledge with real ACT math problems. 1. What is the first term in the arithmetic sequence if terms 6 through 9 are shown below? ...196, 210, 224, 238 7 14 98 126 140 2. What is the sum of the first 8 terms in the arithmetic sequence that begins: 7, 10.5, 14,... 143.5 154 162.5 168 176.5 3. Answers: D, B, E Answer Explanations: 1. As always, we can solve this problem with formulas or via longhand. For the sake of brevity, we will only use one method per problem here. In this case, let us solve our problem via longhand. We are told this is an arithmetic sequence, so we can find our common difference by subtracting neighboring terms. Let us take a pair and subtract to find our $d$. $238 - 224 = 14$ $d = 14$ We know our common difference is 14, and 196 is our 6th term. Let us work backwards to find our 1st term. ___, ___, ___, ___, ___, 196, 210, 224, 238 ___, ___, ___, ___, 182, 196, 210, 224, 238 ___, ___, ___, 168, 182, 196, 210, 224, 238 And so on, until we reach our first term. 126, 140, 154, 168, 182, 196, 210, 224, 238 As long as we kept our work organized, we will find the first term in our sequence. In this case, it is 126. Our final answer is D, 126. 2. Again, we have many options for solving our problem. In this case, we can use a combination of longhand and formula (in addition to the standard options of using either method alone). First, we must find our common difference between our terms by subtracting any neighboring pair. $14 - 10.5 = 3.5$ $d = 3.5$ Now that we have found our $d$, let us finish our sequence until the 8th term by continuing to add 3.5 to each successive term. 7, 10.5, 14, 17.5, 21, 24.5, 28, 31.5 And finally, we can plug in our values into our sum formula to find the sum of all our terms. $(n/2)(a_1 + a_n)$ $(8/2)(7 + 31.5)$ $(4)(38.5)$ $154$ The sum of the first 8 terms in the sequence is 154. Our final answer is B, 154. 3. Again, we can use multiple methods to solve our problem. In this case, let us use our formula for geometric sequences. First, we need to find our common ratio between terms, so let us divide any pair of neighboring terms to find our $r$. ${-27}/9 = -3$ $r = -3$ Now we can plug in our values into our formula. $a_n = a_1( r^{n - 1})$ $a_7 = 1(-3^{7 - 1})$ $a_7 = 1(-3^6)$ $a_7 = 1(-729)$ $a_7 = 729$ The 7th term of our sequence is 729. Our final answer is E, 729. You did it, you genius you! The Take Aways Sequence questions often take a little time and effort to get through, but they are usually made complicated by their number of terms and values rather than being actually difficult to solve. Just remember to keep all your work organized and decide before test-day whether you want to spend your study efforts memorizing, or if you would prefer to work out your sequence problems by hand. As long as you keep your values straight (and don’t get tricked by bait answers!), you will be able to grind through these problems without fail, using either method. What’s Next? Phew! You have officially mastered ACT sequence questions. So...now what? Well you're in luck because there are a lot more ACT math topics and guides to check out! Want to brush up on your ratios? How about your trigonometry? Coordinate geometry and slopes? No matter what ACT topic you want to master, we've got you covered. Feel like you're running out of time on ACT math? Check out our guide to help you beat the clock. Want to know the score you should aim for? Start by looking at how the scoring works and what that means for you. Looking to get a perfect score? Our guide to getting a 36 on ACT math (written by a perfect-scorer) will help you get to where you want to be! Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

Using City Directories for Genealogy Research

Using City Directories for Genealogy Research For anyone researching ancestors in a city or larger community, standard genealogical resources often fall short. Newspapers generally mention only the influential, interesting or most newsworthy residents. Land records offer little help when researching renters. Census records dont tell the stories of individuals who moved multiple times between census years. Cities, however, offer an invaluable historical and genealogical resource not available to those of us researching rural ancestors- namely, city directories. City directories offer anyone conducting family history research in a city or large town a nearly annual census of city residents, as well as a window into the community in which they lived. Genealogists all know the value of placing an ancestor in a particular time and place, but city directories can also be used to follow an individuals occupation, place of employment, and place of residence, as well as potentially identify life events such as marriages and deaths. Looking beyond the names of your ancestors, city directories also provide invaluable insight into your ancestors community, often including sections on neighborhood churches, cemeteries, and hospitals, plus organizations, clubs, associations, and societies. Information Often Found in City Directories Name and occupation of head of household (often men and female widows; later single employed females)Name of spouse (often in parentheses following name of husband; mid to late 19th century)Sometimes the names of children, often only those employed outside the homeStreet name and house number of residenceOccupationWork address (if employed outside the home) Tips for Research in City Directories Abbreviations were often used in city directories to save printing space and costs. Locate (and make a copy) of the list of abbreviations, usually located near the front of the directory, to learn that n Fox St. indicates near Fox St., or that r means resides or, alternatively, rents. Properly translating the abbreviations used in a city directory is essential for correctly interpreting the information it contains. Dont miss the late listing of names received too late for inclusion in the alphabetical portion. This can usually be found located just before or after the alphabetical list of residents and may include people who had recently moved to the area (including those moving within the city limits), as well as individuals the canvasser missed on his initial visit. If youre lucky, you may find a separate list of individuals who migrated from the city (with their new location), or who died within the year. What If I Cant Find My Ancestor? Just who was included in a city directory was up to the discretion of that directorys publisher, and often varied from city to city, or over time. Generally, the earlier the directory, the less information it contains. The earliest directories may list only people of higher status, but directory publishers soon made the attempt to include everyone. Even then, however, not everyone was listed. Sometimes certain parts of town weren’t covered. Inclusion in a city directory was also voluntary (unlike a census), so some people may have chosen not to participate, or were missed because they werent home when the agents came calling. Make sure you have checked every available city directory for the time period when your ancestors were living in the area. People overlooked in one directory may be included in the next. Names were also often misspelled or standardized, so be sure to check name variations. If you can locate a street address for your family from a census, vital, or another record, then many directories also offer a street index. Where to Find City Directories Original and microfilmed city directories can be found in a variety of repositories, and an increasing number are being digitized and made available online. Many may be available either in original format or on microfilm in the library or historical society that covers that particular locality. Many state libraries and historical societies have large city directory collections as well. Major research libraries and archives such as the Library of Congress, Family History Library, and American Antiquarian Society also maintain large collections of microfilmed city directories, for locations across the United States. Over 12,000 city directories for cities across the United States, most from the collection of the Library of Congress, have been microfilmed by Primary Source Media as City Directories of the United States. Their online collection guide lists the cities and directory years included in the collection. The Family History Library Catalog also lists a large collection of city directories, most of which can be borrowed on microfilm for viewing at your local Family History Center. Where to Find Old City Directories Online A large number of city directories can be searched and viewed online, some for free and others as part of various subscription genealogy collections. Large Online City Directory Collections Ancestry.com has one of the largest online collections of city directories, with a focus on coverage between the 1880 and 1900 U.S. federal census, as well as 20th century data. Their U.S. City Directories collection (subscription) offers good search results, but for best results browse directly to the city of interest and then page through the available directories rather than relying on search. The City Directories collection online at subscription-based website Fold3, includes directories for thirty large metropolitan centers in twenty U.S. states. As with the collection at Ancestry.com, better results are achieved by browsing the directories manually rather than relying on search. The Historical Directories Searchable Library is a free website from the University of Leicester in England, with a nice collection of digitized reproductions of local and trade directories for England and Wales for the period 1750–1919. Additional Online Sources for City Directories A number of local and university libraries, state archives and other repositories have digitized city directories and made them available online. Use search terms such as city directory and [your locality name] to find them via your favorite search engine. A number of historical city directories can also be found through online sources for digitized books, such as Internet Archive, Haithi Digital Trust, and Google Books.

Job Materials Portfolio Essay Example | Topics and Well Written Essays - 500 words

Job Materials Portfolio - Essay Example Customer service experience is another mandatory requirement since people to hold this position will have a lot of exposure to the customer. Therefore, one should have the necessary experience to serve customers in a hospitable manner hence making sure that the customer comes back once more. I have chosen to apply for a sales associate in Zara this is because this is the field I have got a lot of experience. In fact, I have studied a course related to sales in the college and this makes me feel that this field can be my best. In fact, I am looking forward to developing my career very much in sales. The opportunity with Zara will give me an opportunity to learn more on what selling really entail. These include selling, restocking and merchandising. Zara is an American company that deals with fashion for both men and women. This means that the company sells clothes to the American population bearing in mind the essence of fashion. For instance, every time designers keep on introducing new fashions in clothes market. This calls for business people to be so keen when it comes to deciding what customers need in order to survive. Zara takes into consideration customers’ preferences in a great way to make sure that their wishes are given priorities when designing their out fits. The company’s mission is to provide excellent customer service. This means that the organization works hard to make sure that they provide perfect services to their customers. This can be achieved through various methods which include involving customers in developing their designs. This means that the organization goes extra miles to make sure that they obtain necessary information from customers in terms of their fashion preferences and tastes. In addition, they use their sales associate to merchandise their stores hence creating a visible image to their customers. Zara Company started its operation in

Reading Response Paper Essay Example | Topics and Well Written Essays - 500 words

Reading Response Paper - Essay Example The author was successful in making the story so vivid for the audience that they were left entranced as if a movie was playing in their heads as narrated by the author of the story. Examples were scenes from the locker room where the men candidly talked about body hair and how it used to be regarded as a badge of manhood. Such topic was not the kind one commonly talks about, but the simple candidness of the dialogue made such a topic so interesting. The audience was very responsive to Harbach, laughing at appropriate times and giving witty side comments to the funny remarks the author read and expressed funnily from the reading of the book. Listening to him read makes one conclude that he knew each and every detail of the story and brought that out in his reading. It was as if he was just talking out loud while writing the book but did not need anyone’s approval to express himself on print. Harbach was a confident reader because he knew his book very well. I have never read the book that the author wrote and read from. However, I felt drawn to the story because the author read it so well. I thought it was also the audience’ first time to get to know about the story but when they asked questions, it was clear that they have read the book beforehand. The author used words that were appropriate to the characters who spoke them. Even the use of curse words depicted the character of the men in the story so well. It was easy to relate to the story especially since this one was read by the author himself, as if he jumped right out of the printed page to make the book come more alive. I was impressed by the richness of the story and the multiple perspectives the author held simultaneously. When the audience asked him questions, I was able to relate more to him as a writer. In the first questions, it seemed that he was thrown off-guard especially because the questions were sensitive, referring to homosexuality. The audience asked him if he derived

Organization Performance Essay -- Business, The Roles of Managers

Organisational Performance. The term organisation performance relates to the past, present and future-projected performance of an organisation, thus, the performance of an organisation comprises the actual output measured against the intended outputs (Goals and Objectives). The role of managers is to ensure that the performance of the organisation is aligned with attaining the goals and objectives of the organisation, by taking necessary steps to ensure that the work (outputs) of an organisation are also aligned with the overall objectives and goals. Organisation Managers’ sets and projects target that are designed or aim to achieving the objectives that are aligned with the mission of the organisations. This also acts as guidance to staffs, which provides the staffs the sense of direction of the organisation. The Performance targets are set/ compare against previous past performances achievement. In order for performance target to be attained, it must be realistic and achievable. Mann (2002) suggested that the key to long term success is having and communicating a clear vision, mission and strategy. Target setting must be specific, measurable, achievable, realistic and time bound with acronym; SMART. Performance indicators are tools device used by organisations to measure how well they are performing in relation to their goals and objectives, thus also provides understanding and indicator to organisations stakeholder on how organisation is in track with achieving its target. Acronym KPI; (key performance indicator) are represented in percentages, often used to express and numeric representation of the organisational performance, thus enables a comparison of attained targets and future target setting. Whilst KPI is an eff... ...alysis of this argument indicates that Strategy can also be derived form actions and reactions of everyone within the organisation. The role of Police environment managers and including the SPCP units’ managers’ primary role are to formulate and implement the predetermined force strategy. Individuality of each managers and external factors can influence the leadership style of individual managers. Organisational managers are individual with recognised authorities, authorized to formulate, delegate and implement existing strategy of an organisation, in order to achieve the objectives of the organisation, the Managers must be competent and motivated in their role, in order to motivate others. The managers of the SPCP units’ steers and direct the staffs within towards achieving the objectives of the Strathclyde Police force objectives of making communities safer. Organization Performance Essay -- Business, The Roles of Managers Organisational Performance. The term organisation performance relates to the past, present and future-projected performance of an organisation, thus, the performance of an organisation comprises the actual output measured against the intended outputs (Goals and Objectives). The role of managers is to ensure that the performance of the organisation is aligned with attaining the goals and objectives of the organisation, by taking necessary steps to ensure that the work (outputs) of an organisation are also aligned with the overall objectives and goals. Organisation Managers’ sets and projects target that are designed or aim to achieving the objectives that are aligned with the mission of the organisations. This also acts as guidance to staffs, which provides the staffs the sense of direction of the organisation. The Performance targets are set/ compare against previous past performances achievement. In order for performance target to be attained, it must be realistic and achievable. Mann (2002) suggested that the key to long term success is having and communicating a clear vision, mission and strategy. Target setting must be specific, measurable, achievable, realistic and time bound with acronym; SMART. Performance indicators are tools device used by organisations to measure how well they are performing in relation to their goals and objectives, thus also provides understanding and indicator to organisations stakeholder on how organisation is in track with achieving its target. Acronym KPI; (key performance indicator) are represented in percentages, often used to express and numeric representation of the organisational performance, thus enables a comparison of attained targets and future target setting. Whilst KPI is an eff... ...alysis of this argument indicates that Strategy can also be derived form actions and reactions of everyone within the organisation. The role of Police environment managers and including the SPCP units’ managers’ primary role are to formulate and implement the predetermined force strategy. Individuality of each managers and external factors can influence the leadership style of individual managers. Organisational managers are individual with recognised authorities, authorized to formulate, delegate and implement existing strategy of an organisation, in order to achieve the objectives of the organisation, the Managers must be competent and motivated in their role, in order to motivate others. The managers of the SPCP units’ steers and direct the staffs within towards achieving the objectives of the Strathclyde Police force objectives of making communities safer.

Caribbean Business Environment

Firstly, here are some of the consequences of regional trade arrangements: Accumulation or growth effects. If closer integration improves the efficiency with which factors are combined it is also likely to induce rater investment. While this additional investment is taking place, countries may experience a medium-term growth effect. If such investment is associated with faster technical progress or accumulation of human capital as identified in the long-run growth rates may also be improved.Investment effects. More emphasis is now given to the impact of regional Integration on production via the effect on foreign direct investment and investment creation and diversion. Transactions costs and regulatory barriers. The traditional theory of customs unions was developed in the context of riff reductions but, as noticed above, the welfare effects of Integration can be quite different If the barriers removed are cost-increasing barriers.Following the SUE experience with Implementing its Si ngle Market program, there Is now greater awareness of the importance of barriers which raise transactions costs in inhibiting trade, and of the value of removing them. Importance of credibility. Many of the effects identified in the modern theory, especially those related to or requiring investment, assume that the integration effort is credible and will not be reversed. If credibility is lacking, and there is uncertainty among investors, their behavior is unlikely to be influenced.The emphasis on credibility assumes the existence of enforcement mechanisms which will ensure the implementation of commitments entered Into when a country Joins a regional Integration scheme. Regional trade agreements reduce the tariffs between the countries which are part of the trade agreement. Regional trade agreements reduce tariffs between countries, but does not allow these countries to Increase tariffs on countries which do not participate. Tariff reductions allow people to purchase goods from ot her countries at lower prices.The gains from learning valuable skills from foreign markets that can subsequently be transferred back to the home country. Integration also has many benefits such as: gains in trade, economies of scale, limited fiscal capabilities and cultural centralization. With deeper levels of integration foreign investment will increase. The lack of resources in the Caribbean will increased more integration and also the people will get to learn other trades from the different countries. Also will adopt and enhance strategies which will help the efficiency and improve competition in the region and the US.

Snow on Arizona SnowBowl Essays - 1668 Words

Snow on Arizona SnowBowl? Works Cited Missing â€Å"A typical Ski season at the Arizona Snow-Bowl lasts from December to Easter† (Arizona SnowBowl Upgrade proposed Action, September 2002, p.2). The Arizona Snow-Bowl, which is located in the San Francisco Peaks, seven miles outside of Flagstaff, Arizona was only open for four days last year! Alarming? Yes, this is why the Arizona Snow bowl has released a fool proof plan, which consists of making their own snow! The Arizona SnowBowl’s fool proof plan is to remodel their whole ski resort. The remodeling would include the building of one new chair lift, the addition of new ski runs, maintenance work on three existing chair lifts, lighting for night time skiing,†¦show more content†¦The evidence that these people are using supports their opinions very clearly. â€Å"Many of these tribes hold true that if this Holy Mountain is disturbed, than so too the fabric of their culture, their spirituality and their livelihood will be disturbed† (SnowBowl Expansion, p.1). The San Francisco Peaks are a sacred place to thirteen tribes in Northern Arizona. The tribes go up to the mountain for religious beliefs, ceremonies, and prayers. Specifically, the tribes pray to the rain gods. If snow machines are put on the mountain, that would defeat the purpose of praying for rain. The holiness of the peaks would be lost for the Native Americans, knowing that their prayers are being disrespected by the Arizona SnowBowl. One aspect of the whole snow making process that people are overlooking is the moral correctness. The unnatural snow created by the snow machines will change the mountain in an unnatural way. By artificially adding reclaimed water to the mountain, the resort disturbs the natural environment, which will inevitably change the terrain of the mountain. Instead we need to learn to accept the natural conditions provided to us, and stop interfering with our fragile environment. The habitat and ecosystem of the San Francisco Peaks is rare. The Mountains are located in the middle of the desert, so theShow MoreRelated Snow on Arizona SnowBowl Essay889 Words   |  4 PagesSnow on Arizona SnowBowl Why would anyone propose to use millions of gallons of water a day to desecrate sacred Indian land, in a State that is going through a drought? Well, the Arizona SnowBowl has proposed to do just that; make artificial snow on their ski resort. The proposal is for their own economical benefit with no respect for the holy San Francisco Peaks, where the Ski resort is located. The San Francisco Peaks are located in Northern Arizona, seven milesRead More We Should Make Snow on the Mountain Essay1064 Words   |  5 PagesWe Should Make Snow on the Mountain The varying opinions on whether snow should be made on the Snowbowl Ski Mountain in Flagstaff, Arizona have grown to become a statewide debate. Snowbowl is one of the sacred mountains in the San Francisco Peaks that is very meaningful to the Native people. If snow were to be made on the mountain, it would interfere with the beliefs of many people. On the other hand, many Arizona residents rely on the ski area for its incoming business, recreation, and for