수열 전체 문제

Determine if a Sequence is Geometric

In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio.

$2,10,50,250,1250,6250,\,\ldots$

Determine if a Sequence is Geometric

In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio.

$72,36,18,9,\frac{9}{2},\frac{9}{4},\,\ldots$

Determine if a Sequence is Geometric

In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio.

$54,18,6,2,\frac{2}{3},\frac{2}{9},\,\ldots$

Determine if a Sequence is Geometric

In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio.

$-3,6,-12,24,-48,96,\,\ldots$

Determine if a Sequence is Geometric

In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio.

$2,-6,18,-54,162,-486,\,\ldots$

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

$48,24,12,6,3,\frac{3}{2},\,\ldots$

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

$12,6,0,-6,-12,-18,\,\ldots$

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

$-7,-2,3,8,13,18,\,\ldots$

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

$5,9,13,17,21,25,\,\ldots$

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

$\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64},\,\ldots$

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

$4,8,12,24,48,96,\,\ldots$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

${a}_{1}=4$ and $r=3$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

${a}_{1}=9$ and $r=2$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

${a}_{1}=-4$ and $r=-2$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

${a}_{1}=-5$ and $r=-3$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

${a}_{1}=27$ and $r=\frac{1}{3}$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

${a}_{1}=64$ and $r=\frac{1}{4}$

*Find the General Term (nth Term) of a Geometric Sequence*

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.

Find ${a}_{11}$ given ${a}_{1}=8$ and $r=3.$

*Find the General Term (nth Term) of a Geometric Sequence*

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.

Find ${a}_{13}$ given ${a}_{1}=7$ and $r=2.$

*Find the General Term (nth Term) of a Geometric Sequence*

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.

Find ${a}_{10}$ given ${a}_{1}=-6$ and $r=-2.$