Find the sum of the infinite geometric series: a) \sum\limits_{n=0}^\infty \left(\frac{1}{2} \right) ^n . (Assume n begins with 1.) You will earn \(1\) penny on the first day, \(2\) pennies the second day, \(4\) pennies the third day, and so on. Find the first term and common difference of a sequence where the third term is 2 and the twelfth term is -25. 5. An employee has a starting salary of $40,000 and will get a $3,000 raise every year for the first 10 years. a_1 = 2, a_(n + 1) = (a_n)/(1 + a_n). The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. If the limit does not exist, then explain why. Fn, for any value of n up to n = 500. \sum_{n = 0}^{\infty}\left ( -\frac{1}{2} \right )^n. document.getElementById("ak_js_1").setAttribute("value",(new Date()).getTime()); Previous post: N4 Grammar: Using tebakari and youda. b) Prove that the sequence is arithmetic. Determinants 9. 1/2, -4/3, 9/4, -16/5, 25/6, cdots, Find the limit of the sequence or state if it diverges. If youd like you can also take the N5 sample questions online. Consider the following sequence: a_1 = 3, \; a_{n+1} = \dfrac{4}{5} -a_n. Question 1. Access the answers to hundreds of Sequences questions that are explained in a way that's easy for you to understand. Web1 Personnel Training N5 Previous Question Papers Pdf As recognized, adventure as without difficulty as experience more or less lesson, amusement, as For example, the following is a geometric sequence. Explain that every monotonic sequence converges. Use the formal definition of the limit of a sequence to prove that the sequence {a_n} converges, where a_n = 5^n + pi. Button opens signup modal. Here are the answers:if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[300,250],'jlptbootcamp_com-medrectangle-4','ezslot_6',115,'0','0'])};__ez_fad_position('div-gpt-ad-jlptbootcamp_com-medrectangle-4-0'); 3) 4 is the correct answer. a_n = n^3 - 3n + 3. 5 + 8 + 11 + + 53. b. x ( n ) = 2 ( n + 3 ) 0.5 ( n + 1 ) 4 ( n 5 ). Determine the convergence or divergence of the sequence with the given nth term. a) Find the nth term. For example, the sum of the first 5 terms of the geometric sequence defined Determine the sum of the following arithmetic series. WebAnswer: Step-by-step explanation: 3n +4 sequence. Use the table feature of a graphing utility to verify your results. WebVIDEO ANSWER: During and stability during instability occurs when a steady state, oh, course. Hint: Write a formula to help you. On day one, a scientist (using a microscope) observes 5 cells in a sample. Calculate this sum in a similar manner: \(\begin{aligned} S_{\infty} &=\frac{a_{1}}{1-r} \\ &=\frac{18}{1-\frac{2}{3}} \\ &=\frac{18}{\frac{1}{3}} \\ &=54 \end{aligned}\). Select one: a. a_n = (-n)^2 b. a_n = (-1)"n c. a_n = ( (-1)^ (n-1)) (n^2) d. a_n Adding \(5\) positive integers is manageable. We can construct the general term \(a_{n}=3 a_{n-1}\) where, \(\begin{aligned} a_{1} &=9 \\ a_{2} &=3 a_{1}=3(9)=27 \\ a_{3} &=3 a_{2}=3(27)=81 \\ a_{4} &=3 a_{3}=3(81)=243 \\ a_{5} &=3 a_{4}=3(243)=729 \\ & \vdots \end{aligned}\). Assume that the pattern continues. Popular Problems. Downvote. Now an+1 = n +1 5n+1 = n + 1 5 5n. \Longrightarrow \left\{\begin{array}{l}{-2=a_{1} r \quad\:\:\:\color{Cerulean}{Use\:a_{2}=-2.}} In this case this is simply their product, \(30\), as they have no common prime factors. (If an answer does not exist, specify.) Determine whether each sequence converges or diverges a) a_n = (1 + 7/n)^n b) b_n = 2^{n - 1}/7^n. 3, 7, 11, 15, 19, Write an expression for the apparent nth term (a_n) of the sequence. https://mathworld.wolfram.com/FibonacciNumber.html. In the previous example the common ratio was 3: This sequence also has a common ratio of 3, but it starts with 2. The increase in money per day stayed constant. Let me know if you have further questions that I can answer for you. How do you find the nth term rule for 1, 5, 9, 13, ? Write out the first ten terms of the sequence. Use the techniques found in this section to explain why \(0.999 = 1\). Given the sequence b^1 = 5. Lets go over the answers: Answer 2, means to rise or ascend, for example to go to the second floor we can say . 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. Furthermore, the account owner adds $12,000 to the account each year after the first. Here \(a_{1} = 9\) and the ratio between any two successive terms is \(3\). Give the first term and the common ratio for the given geometric sequence. If it converges, find the limit. Then find a_{10}. 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}. This section covers how to read the ~100 kanji that are on the N5 exam as well as how to use the vocabulary that is covered at this level. Direct link to Franscine Garcia's post What's the difference bet, Posted 6 years ago. 260, 130, 120, 60,__ ,__, A definite relationship exists among the numbers in the series. In general, \(S_{n}=a_{1}+a_{1} r+a_{1} r^{2}+\ldots+a_{1} r^{n-1}\). Write complete solutions for all the following questions. Write an expression for the apparent nth term of the sequence. a_n = (1 + 2 / n)^{2 n} lim_{n to infinity} a_n, Determine whether the sequence converges or diverges. List the first five terms of the sequence. This means that every term in the sequence is divisible by the lowest common multiple of \(2\), \(3\) and \(5\). Find the nth term of the sequence: 2, 6, 12, 20, 30 Clearly the required sequence is double the one we have found the nth term for, therefore the nth term of the required sequence is 2n(n+1)/2 = n(n + 1). 1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \frac{1}{25}, Write an expression for the apparent nth term (a_n) of the sequence. The home team starts with the ball on the 1-yard line. If the sequence converges, find its limit. Note that the ratio between any two successive terms is \(2\); hence, the given sequence is a geometric sequence. b. In Find all terms between \(a_{1} = 5\) and \(a_{4} = 135\) of a geometric sequence. Login. Unless stated otherwise, formulas above will hold for negative values of If you are looking for a different level of the test I have notes for each level N5, N4, N3, N2, and N1. Web27 Questions Show answers. Write a formula for the general term (the nth term) of this arithmetic sequence. True or false? If the nth term of a sequence is known, it is possible to work out any number in that sequence. Write the first five terms of the sequence \ (3n + 4\). \ (n\) represents the position in the sequence. The first term in the sequence is when \ (n = 1\), the second term in the sequence is when \ (n = 2\), and so on. A. time, like this: What we multiply by each time is called the "common ratio". And because \(\frac{a_{n}}{a_{n-1}}=r\), the constant factor \(r\) is called the common ratio20. 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. Find term 21 of the following sequence. Using the equation above, calculate the 8th term: Comparing the value found using the equation to the geometric sequence above confirms that they match. For the sequences shown: i. Find the indicated nth partial sum of the arithmetic sequence. You might be thinking that is noon and it is, but is slightly more conversational, whereas is more formal or businesslike. WebInstant Solution: Step 1/2 First, let's consider the possible nucleotides for each N position. Plug your numbers into the formula where x is the slope and you'll get the same result: what is the recursive formula for airthmetic formula, It seems to me that 'explicit formula' is just another term for iterative formulas, because both use the same form. Find the limit of the sequence {square root {3}, square root {3 square root {3}}, square root {3 square root {3 square root {3}}}, }, Find a formula for the general term a_n of the sequence. WebTerms of a quadratic sequence can be worked out in the same way. Determine whether the sequence is arithmetic. -2,-8,-18,-32,-50,,an=. Find a formula for the general term, A_n, given the following sequence. a_n = \ln (n + 1) - \ln (n), Determine whether the sequence converges or diverges. Use the table feature of a graphing utility to find the first five terms of the sequence. Cite this content, page or calculator as: Furey, Edward "Fibonacci Calculator" at https://www.calculatorsoup.com/calculators/discretemathematics/fibonacci-calculator.php from CalculatorSoup, What is the sum of the sequence 5, 10, 15, 20, 25, 30, 35, 40, 45, 50? a n = 1 + 8 n n, Find a formula for the sum of n terms. How do you use the direct comparison test for improper integrals? In a sequence, the first term is 82 and the common difference is -21. a_n = (1+3/n)^n. a_n = tan^(-1)(ln 1/n). If it converges, find the limit. Direct link to 's post what dose it mean to crea, Posted 6 years ago. Give the common difference or ratio, if it exists. Assuming \(r 1\) dividing both sides by \((1 r)\) leads us to the formula for the \(n\)th partial sum of a geometric sequence23: \(S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}(r \neq 1)\). \(2,-6,18,-54,162 ; a_{n}=2(-3)^{n-1}\), 7. Write the first five terms of the sequence and find the limit of the sequence (if it exists). As a matter of fact, for all words on the known vocabulary lists for the JLPT, is read as . (a) How many terms are there in the sequence? Step 1/3. Direct link to Alex T.'s post It seems to me that 'expl, Posted 6 years ago. can be used as a prefix though for certain compounds. Also, the triangular numbers formula often comes up. The reason we use a(n)= a+b( n-1 ), is because it is more logical in algebra. The balance in the account after n quarters is given by (a) Compute the first eight terms of this sequence. 0, 3, 8, 15, 24, Each term is the term number times the next term number. In the sequence -1, -5, -9, -13, (a) Is -745 a term? a_n = (2^n)/(2^n + 1). (Assume that n begins with 1.) #|a_{n+1}|/|a_{n}|=((n+1)/(5*5^(n)))/(n/(5^(n)))=(n+1)/(5n)->1/5# as #n->infty#. a n = ( 1 2 n ) n, Find the limits of the following sequence as n . Determine whether the sequence is increasing, decreasing, or not monotonic. 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. Look at the sequence in this table Which function represents the sequence? 21The terms between given terms of a geometric sequence. A structured settlement yields an amount in dollars each year, represented by \(n\), according to the formula \(p_{n} = 6,000(0.80)^{n1}\). Button opens signup modal. For example, if \(a_{n} = (5)^{n1}\) then \(r = 5\) and we have, \(S_{\infty}=\sum_{n=1}^{\infty}(5)^{n-1}=1+5+25+\cdots\). BinomialTheorem 7. a n = cot n 2 n + 3, List the first three terms of each sequence. WebThough you will likely need to use a computer to listen to the audio for the listening section.. First, you should download the: blank answer sheet. a1 = 11/2 , d = 1/2. a_n = (-1)^n(1.001)^n, Determine whether the following sequence converges or diverges. (a) Show that the area A of the squar Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. Example Write the first five terms of the sequence \ (n^2 + 3n - 5\). &=5(5k^2+4k+1). . a. Determine whether the sequence converges or diverges. a_n = (2n - 1)/(n^2 + 4). Web1 Personnel Training N5 Previous Question Papers Pdf As recognized, adventure as without difficulty as experience more or less lesson, amusement, as If it converges, enter the limit as your answer. Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. \(\frac{2}{125}=a_{1} r^{4}\). Can you figure out the next few numbers? Summation (n = 1 to infinity) (-1)^(n-1) by (2n - 1) = Pi by 4. In this form we can determine the common ratio, \(\begin{aligned} r &=\frac{\frac{18}{10,000}}{\frac{18}{100}} \\ &=\frac{18}{10,000} \times \frac{100}{18} \\ &=\frac{1}{100} \end{aligned}\). WebThe general form of an arithmetic sequence can be written as: It is clear in the sequence above that the common difference f, is 2. . Tips: if the sequence is going up in threes (e.g. Note that the ratio between any two successive terms is \(2\). If it converges, find the limit. a_n= (n+1)/n, Find the next two terms of the given sequence. WebVIDEO ANSWER: Okay, so we're given our fallen sequence and we want to find our first term. 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. Use to determine the 100 th term in the sequence. \(\frac{2}{125}=-2 r^{3}\) 1,3,5,7,9, ; a10, Find the cardinal number for the following sets. Direct link to Siegrid Pregartner's post To find the common differ, Posted 5 years ago. n over n + 1. 442 C. 430 D. 439 E. 454. Fundamental Algorithms, Addison-Wesley, 1997, Boston, Massachusetts. 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. Suppose a_n is an always positive sequence and that lim_{n to infinity} a_n diverges. \(1.2,0.72,0.432,0.2592,0.15552 ; a_{n}=1.2(0.6)^{n-1}\). a_n = (1 + 7 / n)^n. . (iii) The sum to infinity of the sequence. If it converges, find the limit. This expression is also divisible by \(3\). 14) a1 = 1 and an + 1 = an for n 1 15) a1 = 2 and an + 1 = 2an for n 1 Answer 16) a1 = 1 and an + 1 = (n + 1)an for n 1 17) a1 = 2 and an + 1 = (n + 1)an / 2 for n 1 Answer How do you use the direct Comparison test on the infinite series #sum_(n=1)^oo(1+sin(n))/(5^n)# ? Note that the ratio between any two successive terms is \(\frac{1}{100}\). Find the sum of the infinite geometric series. Question. Simplify (5n)^2. a_1 = 2, \enspace a_{n + 1} = \dfrac{a_n}{1 + a_n}, Find a formula for the general term a_n of the sequence, assuming that the pattern of the first few terms continues. WebWrite the first five terms of the sequence \ (n^2 + 3n - 5\). List the first five terms of the sequence. Find the first term. WebStudy with Quizlet and memorize flashcards containing terms like 6.1, Which statement describes a geometric sequence?, Use the following partial table of values for a geometric sequence to answer the question. {1/4, 2/9, 3/16, 4/25,}, The first term of a sequence along with a recursion formula for the remaining terms is given below. Step-by-step explanation: Given a) n+5 b)2n-1 Solution for a) n+5 Taking the value of n is 1 we get the first term of the sequence; Similarly taking the value of n 2,3,4 What will be the employee's total earned income over the 10 years? What is the rule for the sequence 3, 5, 8, 13, 21,? Find the general term of a geometric sequence where \(a_{2} = 2\) and \(a_{5}=\frac{2}{125}\). 4, 9, 14, 19, 24, Write the first five terms of the sequence and find the limit of the sequence (if it exists). If it is, find the common difference. (Type an integer or simplified fraction.) Direct link to Tzarinapup's post The reason we use a(n)= a, Posted 6 years ago. If so, calculate it. Webn 1 6. a_1 = 100, a_{25} = 220, n = 25, Write the first five terms of the sequence and find the limit of the sequence (if it exists). (b) What does it mean to say that \displaystyle \lim_{n \to \infty} a_n = 8? What about the other answers? Which of the following formulas can be used to find the terms of the sequence? Find the formula for the nth term of the sequence below. Find the sum of the infinite geometric series. The first six terms of a sequence are 1, 1, 2, 3, 5, 8. &=25k^2+20k+5\\ \{1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \frac{1}{81}, \}. WebThe explicit rule for a sequence is an=5 (2)n1 . Determine whether the sequence converges or diverges. WebFind the sum of the first five terms of the sequence with the given general term. Calculate the \(n\)th partial sum of a geometric sequence. This is equal to \(30\), which obviously is not divisible by any integers greater than itself. a_7 =, Find the indicated term of the sequence. a_1 = 15, d = 4, Write the first five terms of the sequence and find the limit of the sequence (if it exists). This can take the values \(0\), \(1\), \(2\), \(3\), and \(4\). a_n = ((-1)^2n)/(2n)! Find the value of sum of 4*absolute of (-3 - i^2) from i = -1 to 1. You must state if n starts at 0 or 1. The \(n\)th partial sum of a geometric sequence can be calculated using the first term \(a_{1}\) and common ratio \(r\) as follows: \(S_{n}=\frac{a_{1}\left(1-r^{n}\right)}{1-r}\). Extend the series below through combinations of addition, subtraction, multiplication and division. \(a_{n}=-3.6(1.2)^{n-1}, a_{5}=-7.46496\), 13. Explicit formulas can come in many forms. Construct a geometric sequence where \(r = 1\). The function values a1, a2, a3, a4, . triangle. . If it converges, find the limit. If (an) is an increasing sequence and (bn) is a sequence of positive real numbers, then (an.bn) is an increasing sequence. Write the first four terms of the sequence whose general term is given by: an = 4n + 1 a1 = ____? 7, 12, 17, 22, 27. How do you use the direct Comparison test on the infinite series #sum_(n=1)^ooln(n)/n# ? Complex Numbers 5. The nth term of a sequence is 2n^2. If \{a_n\} and \{b_n\} are divergent, then \{a_n + b_n\} is divergent. What is the value of the fifth term? Such sequences can be expressed in terms of the nth term of the sequence. a1 = 8, d = -2, Write the first five terms of the sequence defined recursively. Write the first four terms of the arithmetic sequence with a first term of 5 and a common difference of 3. Use \(a_{1} = 10\) and \(r = 5\) to calculate the \(6^{th}\) partial sum. Determine whether the sequence is decreasing, increasing, or neither. Weba (n) = 5 n 3 o r a n = 5 n 3. (Assume n begins with 0.) In order to find the fifth term, for example, we need to plug, We can get any term in the sequence by taking the first term. Is \left \{ x_n\epsilon_n What are the first five terms of the sequence an = \text{n}^{2} + {2}? Direct link to louisaandgreta's post How do you algebraically , Posted 2 years ago. Similarly to above, since \(n^5-n\) is divisible by \(n-1\), \(n\), and \(n+1\), it must have a factor which is a multiple of \(3\), and therefore must itself be divisible by \(3\). The distances the ball falls forms a geometric series, \(27+18+12+\dots \quad\color{Cerulean}{Distance\:the\:ball\:is\:falling}\). Compute the limit of the following sequence as ''n'' approaches infinity: [2] \: log(1+7^{1/n}). List the first five terms of the sequence. Indexing involves writing a general formula that allows the determination of the nth term of a sequence as a function of n. An arithmetic sequence is a number sequence in which the difference between each successive term remains constant. a. Functions 11. Consider a sequence: 1, 10, 9, x, 25, 26, 49. a_1 = What is the 5^{th} term in the sequence? Suppose that lim_n a_n = L. Prove that lim_n |a_n| = |L|. If lim n |an+1| |an| < 1, the Ratio Test will imply that n=1an = n=1 n 5n converges. If it diverges, enter divergent as your answer. Determine whether the sequence converges or diverges, and, if it converges, find \displaystyle \lim_{n \to \infty} a_n. 7 + 14 + 21 + + 98, Determine the sum of the following arithmetic series. around the world, Direct Comparison Test for Convergence of an Infinite Series. What is the next term in the series 2a, 4b, 6c, 8d, ? Determinants 9. So \(30\) divides every number in the sequence. 2, 5, 8, , 20. 4.2Find lim n a n &=25k^2+20k+4+1\\ 0, -1/3, 2/5, -3/7, 4/9, -5/11, 6/13, What is the 100th term of the sequence a_n = \dfrac{8}{n+1}? 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. (b) What is a divergent sequence? If la_n| converges, then a_n converges. a_n = \frac {(-1)^n}{9\sqrt n}, Determine whether the sequence converges or diverges. \(a_{1}=\frac{3}{4}\) and \(a_{4}=-\frac{1}{36}\), \(a_{3}=-\frac{4}{3}\) and \(a_{6}=\frac{32}{81}\), \(a_{4}=-2.4 \times 10^{-3}\) and \(a_{9}=-7.68 \times 10^{-7}\), \(a_{1}=\frac{1}{3}\) and \(a_{6}=-\frac{1}{96}\), \(a_{n}=\left(\frac{1}{2}\right)^{n} ; S_{7}\), \(a_{n}=\left(\frac{2}{3}\right)^{n-1} ; S_{6}\), \(a_{n}=2\left(-\frac{1}{4}\right)^{n} ; S_{5}\), \(\sum_{n=1}^{5} 2\left(\frac{1}{2}\right)^{n+2}\), \(\sum_{n=1}^{4}-3\left(\frac{2}{3}\right)^{n}\), \(a_{n}=\left(\frac{1}{5}\right)^{n} ; S_{\infty}\), \(a_{n}=\left(\frac{2}{3}\right)^{n-1} ; S_{\infty}\), \(a_{n}=2\left(-\frac{3}{4}\right)^{n-1} ; S_{\infty}\), \(a_{n}=3\left(-\frac{1}{6}\right)^{n} ; S_{\infty}\), \(a_{n}=-2\left(\frac{1}{2}\right)^{n+1} ; S_{\infty}\), \(a_{n}=-\frac{1}{3}\left(-\frac{1}{2}\right)^{n} ; S_{\infty}\), \(\sum_{n=1}^{\infty} 2\left(\frac{1}{3}\right)^{n-1}\), \(\sum_{n=1}^{\infty}\left(\frac{1}{5}\right)^{n}\), \(\sum_{n=1}^{\infty}-\frac{1}{4}(3)^{n-2}\), \(\sum_{n=1}^{\infty} \frac{1}{2}\left(-\frac{1}{6}\right)^{n}\), \(\sum_{n=1}^{\infty} \frac{1}{3}\left(-\frac{2}{5}\right)^{n}\). Sequence: -1, 3 , 7 , 11 ,.. Advertisement Advertisement New questions in Mathematics. - True - False. Use the formula to find the limit as n \to \infty. s (n) = 1 / {n^2} ({n (n + 1)} / 2). a. 5. . Consider the sequence 67, 63, 59, 55 Show that the sequence is arithmetic. For the following sequence, decide whether it converges. 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. If the limit does not exist, then explain why. \(\begin{aligned}-135 &=-5 r^{3} \\ 27 &=r^{3} \\ 3 &=r \end{aligned}\). What kind of courses would you like to see? \(a_{n}=-2\left(\frac{1}{2}\right)^{n-1}\). This sequence has a factor of 3 between each number. 1,\, 4,\, 7,\, 10\, \dots. Suppose that \{ a_n\} is a sequence representing the A retirement account initially has $500,000 and grows by 5% per year. Then use the formula for a_n, to find a_{20}, the 20th term of the sequence. All rights reserved. An arithmetic sequence is defined by U_n=11n-7. &=n(n^2-1)(n^2+1)\\ Math, 14.11.2019 15:23, alexespinosa. c. could, in principle, be continued on and on without end. Answer 3, can mean many things but at the N5 level it probably means to arrive at or to reach a place, which doesnt fit here. Determine whether the sequence is increasing, decreasing, or not monotonic. And is there another term for formulas using the. Determine whether the sequence is divergent or convergent. Find x. a_n = {\cos^2 (n)}/{3^n}, Determine whether the sequence converges or diverges. How do you use the direct Comparison test on the infinite series #sum_(n=1)^ooarctan(n)/(n^1.2)# ? Volume I. Before taking this lesson, make sure you are familiar with the, Here is an explicit formula of the sequence. What is the nth term for the sequence 1, 4, 9, 16, 25, ? Categorize the sequence as arithmetic or geometric, and then calculate the indicated sum. This expression is divisible by \(2\). On the second day of camp I swam 4 laps. Determine if the sequence n^2 e^(-n) converges or diverges. 7, 8, 10, 13, Classify the following sequence as arithmetic, geometric or other. (ii) The 9th term (a_9) of the sequence. 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.
