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.

$5,10,15,20,25,30,\ldots$

Determine if a Sequence is Geometric

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

$112,56,28,14,7,\frac{7}{2},\ldots$

Determine if a Sequence is Geometric

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

$9,-18,36,-72,144,-288,\ldots$

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

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

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

${a}_{1}=128$ and $r=\frac{1}{4}$

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 $r=-3$

*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 ${a}_{9}$ given ${a}_{1}=6$ 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 ${a}_{11}$ given ${a}_{1}=10,000,000$ and $r=0.1.$

In the following exercises, find the indicated term of the given sequence. Find the general term of the sequence.

Find ${a}_{12}$ of the sequence, $6,-24,96,-384,1536,-6144,\ldots$

In the following exercises, find the indicated term of the given sequence. Find the general term of the sequence.

Find ${a}_{9}$ of the sequence, $4374,1458,486,162,54,18,\ldots$

Find the Sum of the First n terms of a Geometric Sequence

In the following exercises, find the sum of the first fifteen terms of each geometric sequence.

$-4,8,-16,32,-64,128\ldots$

Find the Sum of the First n terms of a Geometric Sequence

In the following exercises, find the sum of the first fifteen terms of each geometric sequence.

$3,12,48,192,768,3072\ldots$

Find the Sum of the First n terms of a Geometric Sequence

In the following exercises, find the sum of the first fifteen terms of each geometric sequence.

$3125,625,125,25,5,1\ldots$

In the following exercises, find the sum

$\sum_{i=1}^{8}7{(3)}^{i}$

In the following exercises, find the sum

$\sum_{i=1}^{6}24{\left(\frac{1}{2}\right)}^{i}$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+\frac{1}{81}-\frac{1}{243}+\frac{1}{729}-\ldots$

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

$49+7+1+\frac{1}{7}+\frac{1}{49}+\frac{1}{343}+\ldots$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{8}$

In the following exercises, write each repeating decimal as a fraction.

$0.\overset{-}{36}$

What is the total effect on the economy of a government tax rebate of $\char36 360$ to each household in order to stimulate the economy if each household will spend $60\%$ of the rebate in goods and services?