What will be the employee's total earned income over the 10 years? \(a_{n}=10\left(-\frac{1}{5}\right)^{n-1}\), Find an equation for the general term of the given geometric sequence and use it to calculate its \(6^{th}\) term: \(2, \frac{4}{3},\frac{8}{9}, \), \(a_{n}=2\left(\frac{2}{3}\right)^{n-1} ; a_{6}=\frac{64}{243}\). a n = cot n 2 n + 3, List the first three terms of each sequence. Then, as \(n^5-n\) is divisible by both \(n\) and \(n+1\), it has at least one even factor and must therefore be even (the product of an even integer and any other integer is always even). Assume that the first term in the sequence is a_1: \{\frac{3}{4}, \frac{4}{9}, \frac{5}{16}, \frac{6}{25}, \}. If so, what term is it? Describe the pattern you used to find these terms. Assume n begins with 1. a_n=1/2n^2 [3-2n(n+1)], What is the next number in the sequence? (Assume n begins with 1.) (Assume that n begins with 1.) \left\{\frac{1}{4}, -\frac{4}{5}, \frac{9}{6}, - Find the sum of the first 600 terms. All rights reserved. Write the first five terms of the given sequence where the nth term is given. (a) What is a sequence? pages 79-86, Chandra, Pravin and If the limit does not exist, explain why. An explicit formula directly calculates the term in the sequence that you want. How do you use the direct Comparison test on the infinite series #sum_(n=1)^oo9^n/(3+10^n)# ? Use the passage below to answer the question. . If the limit does not exist, then explain why. 2, 8, 14, 20. a_n = (-1)^n(1.001)^n, Determine whether the following sequence converges or diverges. Here we can see that this factor gets closer and closer to 1 for increasingly larger values of \(n\). If it converges, find the limit. An employee has a starting salary of $40,000 and will get a $3,000 raise every year for the first 10 years. WebGiven the recursive formula for an arithmetic sequence find the first five terms. (Assume n begins with 1.) Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (c) Find the sum of all the terms in the sequence, in terms of n. image is for the answer . Find a formula for the general term of a geometric sequence. If arithmetic or geometric, find t(n). The balance in the account after n quarters is given by (a) Compute the first eight terms of this sequence. And is there another term for formulas using the. Write the first five terms of the arithmetic sequence. Create a scatter plot of the terms of the sequence. Write the first or next four terms of the sequence and make a conjecture about its limit if it converges, or explain why if it diverges. Let V be the set of sequences of real numbers. List the first five terms of the sequence. a_8 = 26, a_{12} = 42, Write the first five terms of the sequence. Sequences & Series 4. \(a_{n}=-\left(-\frac{2}{3}\right)^{n-1}, a_{5}=-\frac{16}{81}\), 9. Is this true? If the sequence converges, find its limit. If it converges, find the limit. ), Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. You get the next term by adding 3 to the previous term. . We have shown that, for all \(n\), \(n^5-n\) is divisible by \(2\), \(3\), and \(5\). True or false? Answer 4, means to enter, but this usually means to enter a room and not a vehicle. Can you add a section on Simplifying Geometric and arithmetic equations? a_1 = 4, a_(n + 1) = 2a_n - 2. Based on this NRICH resource, used with permission. a_n = 1 - n / n^2. What about the other answers? Let a_1 represent the original amount in Find the nth term of a sequence whose first four terms are given. tn=40n-15. Determine whether the sequence converges or diverges. a_1 = 48, a_n = (1/2) a_(n-1) - 8. Then the sequence b_n = 8-3a_n is an always decreasing sequence. a_7 =, Find the indicated term of the sequence. In a sequence that begins 25, 23, 21, 19, 17, , what is the term number for the term with a value of -11? Write the first five terms of the sequence. 100, 400, 200, 800,__ ,__, A definite relationship exists among the numbers in the. Find the fourth term of this sequence. 31) a= a + n + n = 7 33) a= a + n + 1n = 3 35) a= a + n + 1n = 9 37) a= a 4 + 1n = 2 = a a32) + 1nn + 1 = 2 = 3 34) a= a + n + 1n = 10 36) a= a + 9 + 1n = 13 38) a= a 5 + 1n = 3 Explain that every monotonic sequence converges. Show directly from the definition that the sequence \left ( \frac{n + 1}{n} \right ) is a Cauchy sequence. a_n = (2n - 1)(2n + 1). For the geometric sequence 5 / 3, -5 / 6, 5 / {12}, -5 / {24}, . a_n = (1 + 7 / n)^n. . Browse through all study tools. Find all terms between \(a_{1} = 5\) and \(a_{4} = 135\) of a geometric sequence. This expression is divisible by \(2\). The t Write a formula for the general term or nth term for the sequence. \left\{\begin{matrix} a(1)=-11\\ a(n)=a(n-1)\cdot 10 \end{matrix}\right. Given the sequence b^1 = 5. Simplify (5n)^2. BinomialTheorem 7. If so, then find the common difference. Find the first five terms of the sequence a_n = (-\frac{1}{5})^n. Determinants 9. Rewrite the first five terms of the arithmetic sequence. a_n = \frac{1 + (-1)^n}{n}, Use the table feature of a graphing utility to find the first 10 terms of the sequence. WebFind the next number in the sequence (using difference table ). an=2 (an1) a1=5 Akim runs 1.75 miles on his first day of training for a road race. Determine whether the sequence converges or diverges. a_n = \dfrac{5+2n}{n^2}. Assume n begins with 1. a_n = n/(n^2+1), Write the first five terms of the sequence. A. To show that the sequence { n 5 + 2 n n 2 } diverges to infinity as n approaches infinity, we need to show that the terms of the sequence get arbitrarily large as n gets arbitrarily large. 4) 2 is the correct answer. Suppose a_n is an always increasing sequence. Show that, for every real number y, there is a sequence of rational numbers which converges to y. a_n = 1 - 10^(-n), n = 1, 2, 3, Write the first or next four terms of the following sequences. n however, it could be easier to find Fn and solve for . \left\{1, \frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \frac{1}{9}, \dots \right\}. 436 B. Math, 14.11.2019 15:23, alexespinosa. 2) A monotone sequence that is not Cauchy. Given that \frac{1}{1 - x} = \sum\limits_{n = 0}^{\infty}x^n if -1 less than x less than 1, find the sum of the series \sum\limits_{n = 1}^{\infty}\frac{n^2}{ - \pi^n}. c) a_n = 0.2 n +3 . You are often asked to find a formula for the nth term. Find the limit of the following sequence: c_n = \left ( \dfrac{n^2 + n - 6}{n^2 - 2n - 2} \right )^{5n+2}. \(\frac{2}{125}=-2 r^{3}\) a_n = (-1)^{n-1} (n(n - 1)). Assume n begins with 1. a_n = (2/n)(n + (2/n)(n(n - 1)/2 - n)). \(1-\left(\frac{1}{10}\right)^{6}=1-0.00001=0.999999\). (Bonus question) A sequence {a n } is given by a 1 = 2 , a n + 1 = 2 + a n . For this first section, you just have to choose the correct hiragana for the underlined kanji. The nth term of a sequence is given. 200, 100, 500, 250, 1,250,__ ,__, Which one of the numbers does not belong in the following sequence; 2, - 3, - 6, - 7, - 8, - 14, - 15, - 30? State the test used. Furthermore, the account owner adds $12,000 to the account each year after the first. (If an answer does not exist, specify.) Transcribed Image Text: 2.2.4. Was immer er auch probiert, um seinen unverwechselbaren Platz im Rudel zu finden - immer ist ein anderer geschickter, klger Then uh steady state stable in the -92, -85, -78, -71, What is the 12th term in the following sequence? The pattern is continued by multiplying by 0.5 each time, like this: What we multiply by each time is called the "common ratio". Is \left \{ x_n\epsilon_n What are the first five terms of the sequence an = \text{n}^{2} + {2}? From In a sequence, the first term is 82 and the common difference is -21. Find an equation for the general term of the given geometric sequence and use it to calculate its \(10^{th}\) term: \(3, 6, 12, 24, 48\). What is the rule for the sequence 3, 5, 8, 13, 21,? In an arithmetic sequence, a17 = -40 and a28 = -73. The partial sum up to 4 terms is 2+3+5+7=17. For example, . The total distance that the ball travels is the sum of the distances the ball is falling and the distances the ball is rising. a. All other trademarks and copyrights are the property of their respective owners. \(a_{n}=r a_{n-1} \quad\color{Cerulean}{Geometric\:Sequence}\). a_n = (-2)^{n + 1}. Determine whether the sequence converges or diverges. On day two, the scientist observes 11 cells in the sample. since these terms are positive. a. Use the pattern to write the nth term of the sequence as a function of n. a_1=81, a_k+1 = 1/3 a_k, Write the first five terms of the sequence. Theory of Equations 3. Determine whether each sequence is arithmetic or not if yes find the next three terms. a_n = \left(-\frac{3}{4}\right)^n, n \geq 1, Find the limit of the sequence. n^2+1&=(5k+2)^2+1\\ b) a_n = 5 + 2n . Therefore, \(0.181818 = \frac{2}{11}\) and we have, \(1.181818 \ldots=1+\frac{2}{11}=1 \frac{2}{11}\). Write complete solutions for all the following questions. If it converges, find the limit. In your own words, describe the characteristics of an arithmetic sequence. In a number sequence, the order of the sequence is important, and depending on the sequence, it is possible for the same terms to appear multiple times. If you're seeing this message, it means we're having trouble loading external resources on our website. a_n = cos (n / 7). Use this and the fact that \(a_{1} = \frac{18}{100}\) to calculate the infinite sum: \(\begin{aligned} S_{\infty} &=\frac{a_{1}}{1-r} \\ &=\frac{\frac{18}{100}}{1-\left(\frac{1}{100}\right)} \\ &=\frac{\frac{18}{100}}{\frac{90}{100}} \\ &=\frac{18}{100} \cdot \frac{100}{99} \\ &=\frac{2}{11} \end{aligned}\). If converge, compute the limit. this, Posted 6 years ago. 1,\, 4,\, 7,\, 10\, \dots. Compute the first five terms of the sequence using the format for a dynamical system defined by a difference equation: Delta t_n = 1.5(100 - t_n), t_0 = 200. (Assume n begins with 1.). For example, the sum of the first 5 terms of the geometric sequence defined \\ {\frac{2}{125}=a_{1} r^{4} \quad\color{Cerulean}{Use\:a_{5}=\frac{2}{125}.}}\end{array}\right.\). Find an equation for the nth term of the arithmetic sequence. Find a formula for the general term an of the sequence starting with a1: 4/10, 16/15, 64/20, 256/25,. Find a formula for the general term, a_n. This is the same format you will use to submit your final answers on the JLPT. arrow_forward What term in the sequence an=n2+4n+42 (n+2) has the value 41? Determine if the following sequence converges or diverges. SEVEN C. EIGHT D. FIFTEEN E. THIRTY. Complete the recursive formula of the arithmetic sequence 1, 15, 29, 43, . a(1) = ____ a(n) = a(n - 1)+ ____, Complete the recursive formula of the arithmetic sequence 14, 30, 46, 62, . d(1) = ____ d(n) = d(n - 1)+ ____, Complete the recursive formula of the arithmetic sequence -15, -11, -7, -3, . (a) c(1) = ____ (b) c(n) = c(n - 1) + ____. -7, -4, -1, What is the 7th term of the following arithmetic sequence? If the limit does not exist, then explain why. How do you use the direct Comparison test on the infinite series #sum_(n=2)^oon^3/(n^4-1)# ? What is the common difference, and what are the explicit and recursive formulas for the sequence? Determine if the sequence {a_n} converges, and if it does, find its limit when a_n = dfrac{6n+(-1)^n}{4n+2}. Step 1/3. Your shortcut is derived from the explicit formula for the arithmetic sequence like 5 + 2(n 1) = a(n). Can't find the question you're looking for? \(a_{n}=8\left(\frac{1}{2}\right)^{n-1}, a_{5}=\frac{1}{2}\), 7. How do you use basic comparison test to determine whether the given series converges or diverges See all questions in Direct Comparison Test for Convergence of an Infinite Series. Ive made a handy dandy PDF of this post available at the end, if youd like to just print this out for when you study the test. A. c a g g a c B. c t g c a g C. t a g g t a D. c c t c c t. Determine if the sequence is convergent or divergent. A certain ball bounces back at one-half of the height it fell from. Select one: a. a_n = (-n)^2 b. a_n = (-1)"n c. a_n = ((-1)^(n-1))(n^2) d. a_n =(-1)^n square root of n. Find the 4th term of the recursively defined sequence. What is the dollar amount? Determine if the sequence n^2 e^(-n) converges or diverges. Number Sequences. The sequence \left \{a_n = \frac{1}{n} \right \} is Cauchy because _____. Lets take a look at the answers:if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[580,400],'jlptbootcamp_com-medrectangle-3','ezslot_4',103,'0','0'])};__ez_fad_position('div-gpt-ad-jlptbootcamp_com-medrectangle-3-0'); 1) 1 is the correct answer. Substitute \(a_{1} = \frac{-2}{r}\) into the second equation and solve for \(r\). There are multiple ways to denote sequences, one of which involves simply listing the sequence in cases where the pattern of the sequence is easily discernible. . a) the sequence converges with limit = dfrac{7}{4} b) the sequence converges with lim How many positive integers between 22 and 121, inclusive, are divisible by 4? a_1 = 6, a_(n + 1) = (a_n)/n. A) a_n = a_{n - 1} + 1 B) a_n = a_{n - 1} + 2 C) a_n = 2a_{n - 1} -1 D) a_n = 2a_{n - 1} - 3. The common difference could also be negative: This common difference is 2 24An infinite geometric series where \(|r| < 1\) whose sum is given by the formula:\(S_{\infty}=\frac{a_{1}}{1-r}\). In general, \(S_{n}=a_{1}+a_{1} r+a_{1} r^{2}+\ldots+a_{1} r^{n-1}\). Find the general term, a_n, for the given seque Write the first five terms of the sequence: c_1 = 5, c_n = -2c_{n - 1} + 1. \(\frac{2}{125}=a_{1} r^{4}\). A + B(n-1) is the standard form because it gives us two useful pieces of information without needing to manipulate the formula (the starting term A, and the common difference B). The pattern is continued by adding 3 to the last number each time, like this: This sequence has a difference of 5 between each number. a) 2n-1 b) 7n-2 c) 4n+1 d) 2n^2-1. centered random scalars with finite variance. {1, 4, 9, 16, 25, 36}. If \{a_n\} and \{b_n\} are divergent, then \{a_n + b_n\} is divergent. WebTitle: 65.pdf Author: Mo Created Date: 5/22/2016 1:00:55 AM This formula allows us to simply plug in the number of the term we are interested in, and we will get the value of that term. Web5) 1 is the correct answer. If the limit does not exist, explain why. \(a_{n}=2\left(\frac{1}{4}\right)^{n-1}, a_{5}=\frac{1}{128}\), 5. can be used as a prefix though for certain compounds. a_n = square root {n + square root {n + 1}} - square root n, Find the limits of the following sequence as n . An initial roulette wager of $\(100\) is placed (on red) and lost. A series is convergent if the sequence converges to some limit, while a sequence that does not converge is divergent. a_n = n^3 - 3n + 3. \sum_{n = 0}^{\infty}\left ( -\frac{1}{2} \right )^n. Find the 5th term in the sequence See answer Advertisement goodLizard Answer: 15 Step-by-step explanation: (substitute 5 in Then use the formula for a_n, to find a_{20}, the 20th term of the sequence. if lim n { n 5 + 2 n n 2 } = , then { n 5 + 2 n n 2 } diverges to infinity. Basic Math. Determine the sum of the following arithmetic series. Therefore, the ball is falling a total distance of \(81\) feet. This sequence starts at 1 and has a common ratio of 2. Assume n begins with 1. a_n = ((-1)^n)/n, Write the first five terms of the sequence and find the limit of the sequence (if it exists). -4 + -7 + -10 + -13. Web(Band 5) Wo die Geschichten wohnen - 2017-01-27 Kunst und die Bibel - Francis A. Schaeffer 1981 Winzling - Marion Dane Bauer 2005 Winzling ist der bei weitem kleinste und schwchste Welpe im Wolfsrudel. 1, 3, \frac{9}{2}, \frac{9}{2}, \frac{27}{8}, \frac{81}{40}, (A) \frac{77}{80} \\(B) \frac{79}{80} \\(C) \frac{81}{80} \\(D) \frac{83}{80} \\(E) \frac{87} Find a formula for the nth term of the sequence in terms of n. 1, 0, 1, 0, 1, \dots, Compute the sum: \sum_{i \in S} \left(i^2 + 1\right) where S = \{1, 3, 5, 7\}. A geometric series is the sum of the terms of a geometric sequence. Use the formula to find the limit as n \to \infty. List the first four terms of the sequence whose nth term is a_n = (-1)^n + 1 / n. Solve the recurrence relation a_n = 2a_n-1 + 8a_n-2 with initial conditions a_0 = 1, a_1 = 4. Determine whether the sequence is arithmetic. a_n = \frac {\cos^2 (n)}{2^n}, Determine whether the sequence converges or diverges. This might lead to some confusion as to why exactly you missed a particular question. Predict the product from the reaction of substance (reddish-brown = Br) with Br_2, FeBr_3. an=2n+1 arrow_forward In the expansion of (5x+3y)n , each term has the form (nk)ankbk ,where k successively takes on the value 0,1,2.,n. If (nk)= (72) what is the corresponding term? On the first day of camp I swam 2 laps. a_1 = 12 and a_(k+1)= a_k + 4, Find the indicated term of the sequence. If \{a_n\} is decreasing and a_n greater than 0 for all n, then \{a_n\} is convergent. What is U_1 and d? A nonlinear system with these as variables can be formed using the given information and \(a_{n}=a_{1} r^{n-1} :\): \(\left\{\begin{array}{l}{a_{2}=a_{1} r^{2-1}} \\ {a_{5}=a_{1} r^{5-1}}\end{array}\right. This is probably the easiest section of the test to study for because it simply involves a lot of memorization of key words. , 6n + 7. In the sequence above, the first term is 12^{10} and each term after the first is 12^{10} more than the preceding term. High School answered F (n)=2n+5. Also, the triangular numbers formula often comes up. As \(k\) is an integer, \(5k^2+4k+1\) is also an integer, and so \(n^2+1\) is a multiple of \(5\). So you get a negative 3/7, and The sum of the first n terms of an infinite sequence is 3n2 + 5n 2 for all n belongs to Z+. (Assume n begins with 1. around the world, Direct Comparison Test for Convergence of an Infinite Series. Construct a geometric sequence where \(r = 1\). A _____________sequence is a sequence of numbers in which the ratio between any two consecutive terms is a constant. Continue inscribing squares in this manner indefinitely, as pictured: \(\frac{4}{3}, \frac{8}{9}, \frac{16}{27}, \dots\), \(\frac{1}{6},-\frac{1}{6},-\frac{1}{2}, \ldots\), \(\frac{1}{3}, \frac{1}{4}, \frac{3}{16}, \dots\), \(\frac{1}{2}, \frac{1}{4}, \frac{1}{6} \dots\), \(-\frac{1}{10},-\frac{1}{5},-\frac{3}{10}, \dots\), \(a_{n}=-2\left(\frac{1}{7}\right)^{n-1} ; S_{\infty}\), \(\sum_{n=1}^{\infty} 5\left(-\frac{1}{2}\right)^{n-1}\). Question. Direct link to Jerry Nilsson's post 3 + 2( 1) To make up the difference, the player doubles the bet and places a $\(200\) wager and loses. If the remainder is \(4\), then \(n+1\) is divisible by \(5\), and then so is \(n^5-n\), as it is divisible by \(n+1\). a_n = {7 + 2 n^2} / {n + 7 n^2}, Determine if the given sequence converges or diverges. If the limit does not exist, then explain why. triangle. The answers to today's Quordle Daily Sequence, game #461, are SAVOR SHUCK RURAL CORAL Quordle answers: The past 20 Quordle #460, Saturday 29 . If it converges, enter the limit as your answer. This is very simple to do if you could just see it written in kanji (yesterday night). Write the first four terms of the arithmetic sequence with a first term of 5 and a common difference of 3. The main thing to notice in your sequence is that there are actually 2 different patterns taking place --- one in the numerator and one in the denominator. If you are looking for a different level of the test I have notes for each level N5, N4, N3, N2, and N1. (Assume that n begins with 1.) \sum_{n = 0}^\infty \frac{2^n + 3^n}{5^{n + 1}} = \frac{5}{6}. The distances the ball rises forms a geometric series, \(18+12+8+\cdots \quad\color{Cerulean}{Distance\:the\:ball\:is\:rising}\). Simply put, this means to round up or down to the closest integer. If a_n is a sequence and limit (n tends to infinity) a_n = infinity, then the sequence diverges. If it converges, find the limit. If the limit does not exist, then explain why. So again, \(n^2+1\) is a multiple of \(5\), meaning that \(n^5-n\) is too. Find an expression for the n^{th} term of the sequence. Now #a_{n+1}=(n+1)/(5^(n+1))=(n+1)/(5*5^(n))#. We can construct the general term \(a_{n}=3 a_{n-1}\) where, \(\begin{aligned} a_{1} &=9 \\ a_{2} &=3 a_{1}=3(9)=27 \\ a_{3} &=3 a_{2}=3(27)=81 \\ a_{4} &=3 a_{3}=3(81)=243 \\ a_{5} &=3 a_{4}=3(243)=729 \\ & \vdots \end{aligned}\). a_n = (1 + \frac 5n)^n, Determine whether the sequence converges or diverges. where \(a_{1} = 27\) and \(r = \frac{2}{3}\). If the theater is to have a seating capacity of 870, how many rows must the architect us Find the nth term of the sequence: 1 / 2, 1 / 4, 1 / 4, 3 / 8, . (b) What is a divergent sequence? &=25m^2+30m+10\\ I do think they are still useful to go through in order to get an idea of how the test will be conducted, though.if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[728,90],'jlptbootcamp_com-box-3','ezslot_2',102,'0','0'])};__ez_fad_position('div-gpt-ad-jlptbootcamp_com-box-3-0'); The only problem with these practice tests is that they dont come with any answer explanations. Apply the product rule to 5n 5 n. 52n2 5 2 n 2. Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the graph of the sequence by hand. If this remainder is \(1\), then \(n-1\) is divisible by \(5\), and then so is \(n^5-n\), as it is divisible by \(n-1\). The following list shows the first six terms of a sequence. 7, 12, 17, 22, 27. Is the sequence bounded? When it converges, estimate its limit. If the sequence is not arithmetic or geometric, describe the pattern. 3, 7, 11, 15, 19, Write an expression for the apparent nth term (a_n) of the sequence. .? On the second day of camp I swam 4 laps. For the sequences shown: i) Find the next 2 numbers in the sequence ii) Write the rule to explain the link between consecutive terms in the form [{MathJax fullWidth='false' a_{n+1}=f(a_n) }] iii) Find a formula for the general term and of the sequence, assuming that the pattern of the first few terms continues. The sum of the first 20 terms of an arithmetic sequence with a common difference of 3 is 650. Write out the first ten terms of the sequence. {a_n} = {{{x^n}} \over {n! Test your understanding with practice problems and step-by-step solutions. \{ \frac{1}{4}, \frac{-2}{9}, \frac{3}{16}, \frac{-4}{25}, \}, Find a formula for the general term and of the sequence, assuming that the pattern of the first few terms continues. If it converges, find the limit. If the ball is initially dropped from \(8\) meters, approximate the total distance the ball travels. Direct link to Franscine Garcia's post What's the difference bet, Posted 6 years ago. The day after that, he increases his distance run by another 0.25 miles, and so on. 45, 50, 65, 70, 85, dots, The graph of an arithmetic sequence is shown. a_n = \frac{n}{n + 1}, Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. Determine whether the following sequence converges or diverges. This ratio is called the ________ ratio. If it converges, find the limit. Consider the \(n\)th partial sum of any geometric sequence, \(S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}=\frac{a_{1}}{1-r}\left(1-r^{n}\right)\). . (Assume that n begins with 1.) b. What is the value of the fifth term? is almost always pronounced . There are also many special sequences, here are some of the most common: This Triangular Number Sequence is generated from a pattern of dots that form a Use this to determine the \(1^{st}\) term and the common ratio \(r\): To show that there is a common ratio we can use successive terms in general as follows: \(\begin{aligned} r &=\frac{a_{n}}{a_{n-1}} \\ &=\frac{2(-5)^{n}}{2(-5)^{n-1}} \\ &=(-5)^{n-(n-1)} \\ &=(-5)^{1}\\&=-5 \end{aligned}\).

Metris Camper Conversion Kit, Svu Dodds Memo, Articles N