12.7.2: Practice Test

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Practice Test

In the following exercises, write the first five terms of the sequence whose general term is given.

320.

$a_{n} = \frac{5 n - 3}{3^{n}}$

321.

$a_{n} = \frac{(n + 2)!}{(n + 3)!}$

322.

Find a general term for the sequence, $- \frac{2}{3}, - \frac{4}{5}, - \frac{6}{7}, - \frac{8}{9}, - \frac{10}{11}, …$

323.

Expand the partial sum and find its value. $\sum_{i = 1}^{4} {(−4)}^{i}$

324.

Write the following using summation notation. $−1 + \frac{1}{4} - \frac{1}{9} + \frac{1}{16} - \frac{1}{25}$

325.

Write the first five terms of the arithmetic sequence with the given first term and common difference. $a_{1} = − 13$ and $d = 3$

326.

Find the twentieth term of an arithmetic sequence where the first term is two and the common difference is $−7 .$

327.

Find the twenty-third term of an arithmetic sequence whose seventh term is $11$ and common difference is three. Then find a formula for the general term.

328.

Find the first term and common difference of an arithmetic sequence whose ninth term is $−1$ and the sixteenth term is $−15 .$ Then find a formula for the general term.

329.

Find the sum of the first 25 terms of the arithmetic sequence, $5, 9, 13, 17, 21, …$

330.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is $a_{n} = −3 n + 100 .$

331.

Find the sum. $\sum_{i = 1}^{40} (5 i - 21)$

In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio.

332.

$14, 3, −8, −19, −30, −41, …$

333.

$324, 108, 36, 12, 4, \frac{4}{3}, …$

334.

Write the first five terms of the geometric sequence with the given first term and common ratio. $a_{1} = 6$ and $r = −2$

335.

In the geometric sequence whose first term and common ratio are $a_{1} = 5$ and $r = 4,$ find $a_{11} .$

336.

Find $a_{10}$ of the geometric sequence, $1250, 250, 50, 10, 2, \frac{2}{5}, … .$ Then find a formula for the general term.

337.

Find the sum of the first thirteen terms of the geometric sequence, $2, −6, 18, −54, 162, −486 …$

In the following exercises, find the sum.

338.

$\sum_{i = 1}^{9} 5 {(2)}^{i}$

339.

$1 - \frac{1}{5} + \frac{1}{25} - \frac{1}{125} + \frac{1}{625} - \frac{1}{3125} + …$

340.

Write the repeating decimal as a fraction. $0. \overset{—}{81}$

341.

Dave just got his first full-time job after graduating from high school at age 18. He decided to invest $450 per month in an IRA (an annuity). The interest on the annuity is 6% which is compounded monthly. How much will be in Adam’s account when he retires at his sixty-fifth birthday?

342.

Expand the binomial using Pascal’s Triangle. ${(m - 2 n)}^{5}$

343.

Evaluate each binomial coefficient. ⓐ $(\begin{matrix} 8 \\ 1 \end{matrix})$
ⓑ $(\begin{matrix} 16 \\ 16 \end{matrix})$ ⓒ $(\begin{matrix} 12 \\ 0 \end{matrix})$ ⓓ $(\begin{matrix} 10 \\ 6 \end{matrix})$

344.

Expand the binomial using the Binomial Theorem. ${(4 x + 5 y)}^{3}$

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