Practice Test

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

Expand the partial sum and find its value. ${\displaystyle \sum _{i=1}^4{(\mathrm{-4})}^i}$

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 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 sum of the first 25 terms of the arithmetic sequence, $5,9,13,17,21,\text{…}$

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

$324,108,36,12,4,\frac{4}{3},\text{…}$

In the geometric sequence whose first term and common ratio are $a_1=5$ and $r=4,$ find $a_{11}.$

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

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

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?

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