answers }, Find a formula for the nth term, an, of the sequence assuming that the indicated pattern continues. . Determine whether the following sequence converges or diverges. a n = n n + 1 2. Direct link to Jack Liebel's post Do you guys like meth , Posted 2 years ago. 45, 50, 65, 70, 85, dots, The graph of an arithmetic sequence is shown. \sum_{n = 0}^{\infty}\left ( -\frac{1}{2} \right )^n. \left\{\frac{1}{4}, -\frac{4}{5}, \frac{9}{6}, - Find the sum of the first 600 terms. If it converges, find the limit. In your own words, describe the characteristics of an arithmetic sequence. Use this and the fact that \(a_{1} = \frac{18}{100}\) to calculate the infinite sum: \(\begin{aligned} S_{\infty} &=\frac{a_{1}}{1-r} \\ &=\frac{\frac{18}{100}}{1-\left(\frac{1}{100}\right)} \\ &=\frac{\frac{18}{100}}{\frac{90}{100}} \\ &=\frac{18}{100} \cdot \frac{100}{99} \\ &=\frac{2}{11} \end{aligned}\). 1, (1/2), (1/6), (1/24), (1/120) Write the first five terms of the sequence. Let a_n = \frac{(1 + \sqrt{5})^n - (1 - \sqrt{5})^n}{2^n \sqrt{5}} be a sequence with nth term an. - True - False. . \(\begin{aligned} a_{n} &=a_{1} r^{n-1} \\ a_{n} &=-5(3)^{n-1} \end{aligned}\). Is \left \{ x_n\epsilon_n What are the first five terms of the sequence an = \text{n}^{2} + {2}? Find the seventh term of the sequence. sequence 3, 6, 9, 12), there will probably be a three in the formula, etc. Unless stated otherwise, formulas above will hold for negative values of Using the equation above, calculate the 8th term: Comparing the value found using the equation to the geometric sequence above confirms that they match. Find the general term of a geometric sequence where \(a_{2} = 2\) and \(a_{5}=\frac{2}{125}\). a_n = (2n - 1)(2n + 1). Find x. Question: Determine the limit of the sequence: 50, 48, 46, 44, 42, Write the first five terms of the sequence and find the limit of the sequence (if it exists). BinomialTheorem 7. An explicit formula directly calculates the term in the sequence that you want. Subtracting these two equations we then obtain, \(S_{n}-r S_{n}=a_{1}-a_{1} r^{n}\) 7, 8, 10, 13, Classify the following sequence as arithmetic, geometric or other. Now #a_{n+1}=(n+1)/(5^(n+1))=(n+1)/(5*5^(n))#. The sequence \left \{a_n = \frac{1}{n} \right \} is Cauchy because _____. An initial roulette wager of $\(100\) is placed (on red) and lost. Write out the first ten terms of the sequence. True or false? Your answer will be in terms of n. (b) What is the second-to-last term? Accessibility StatementFor more information contact us atinfo@libretexts.org. I personally use all of these on a daily basis and highly recommend them. Introduction \{ \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. 4. Web1 Personnel Training N5 Previous Question Papers Pdf As recognized, adventure as without difficulty as experience more or less lesson, amusement, as
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