수열 전체 문제

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

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

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

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

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

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

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

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

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

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 $-1$ and the sixteenth term is $-15.$ Then find a formula for the general term.

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

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

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

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

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.

$14,3,-8,-19,-30,-41,\ldots$

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.

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

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

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, $1250,250,50,10,2,\frac{2}{5},\ldots .$ Then find a formula for the general term.

Find the sum of the first thirteen terms of the geometric sequence, $2,-6,18,-54,162,-486\ldots$

In the following exercises, find the sum.

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

In the following exercises, find the sum.

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

In the following exercises, find the sum.

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