Chapter 9.3, Problem 35E

To determine

To find: the n^th term of the geometric sequence.

Answer to Problem 35E

The n^thterm of the geometric sequence will be $a_n=9{\left(2\right)}^{n-1}$ .

Explanation of Solution

Given information:

Three terms of the sequence are given by,

  $9,18,36,\mathrm{...}$

Calculation:

The general term of geometric sequence is given by formula

  $a_n=a_1{r}^{n-1}$

Here, $a_1$ is the first term and $r$ is common ratio.

Now $a_2=a_1{r}^{2-1}$

  $\begin{array}{l}18=9r\\ r=\frac{18}{9}\\ r=\mathrm{2...............}(1)\end{array}$

Now, calculate the value of $a_n$ by using the formula as shown:

  $\begin{array}{c}{a}_n=a_1{r}^{n-1}\\ a_n=9{\left(2\right)}^{n-1}\end{array}$

Hence, the n^thterm will be $a_n=9{\left(2\right)}^{n-1}$ .