Chapter 9.3, Problem 39E

To determine

To find: the 8^th term of the geometric sequence.

Answer to Problem 39E

The 8^thterm of the geometric sequence will be $a_8=13122$ .

Explanation of Solution

Given information:

Three terms of the sequence are given by,

  $6,18,54,\mathrm{...}$

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

  $\begin{array}{l}18=6r\\ r=\frac{18}{6}\\ r=\mathrm{3...............}(1)\end{array}$

Now, calculate the value of $a_8$ by using the formula as shown:

  $\begin{array}{c}{a}_8=a_1{r}^{8-1}\\ a_8=a_1{r}^7\\ a_8=6\times {\left(3\right)}^7\\ a_8=13122\end{array}$

Hence, the 8^thterm will be $a_8=13122$ .