### Practice Test

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

${a}_{n}=\frac{5n-3}{{3}^{n}}$

Find a general term for the sequence, $-\frac{2}{3},-\frac{4}{5},-\frac{6}{7},-\frac{8}{9},-\frac{10}{11},\text{\u2026}$

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

Write the first five terms of the arithmetic sequence with the given first term and common difference. ${a}_{1}=\mathrm{-13}$ and $d=3$

Find the twentieth term of an arithmetic sequence where the first term is two and the common difference is $\mathrm{-7}.$

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.

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

Find the sum of the first 50 terms of the arithmetic sequence whose general term is ${a}_{n}=\mathrm{-3}n+100.$

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.

$14,3,\mathrm{-8},\mathrm{-19},\mathrm{-30},\mathrm{-41},\text{\u2026}$

Write the first five terms of the geometric sequence with the given first term and common ratio. ${a}_{1}=6$ and $r=\mathrm{-2}$

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

Find ${a}_{10}$ of the geometric sequence, $1250,250,50,10,2,\frac{2}{5},\text{\u2026}\text{.}$ Then find a formula for the general term.

Find the sum of the first thirteen terms of the geometric sequence, $2,\mathrm{-6},18,\mathrm{-54},162,\mathrm{-486}\text{\u2026}$

In the following exercises, find the sum.

$\sum _{i=1}^{9}5{\left(2\right)}^{i}$

Write the repeating decimal as a fraction. $0.\stackrel{\u2014}{81}$

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?

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

Evaluate each binomial coefficient. ⓐ $\left(\begin{array}{c}8\hfill \\ 1\hfill \end{array}\right)$

ⓑ $\left(\begin{array}{c}16\hfill \\ 16\hfill \end{array}\right)$ ⓒ $\left(\begin{array}{c}12\hfill \\ 0\hfill \end{array}\right)$ ⓓ $\left(\begin{array}{c}10\hfill \\ 6\hfill \end{array}\right)$

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