Chapter 12.3, Problem 17AYU

To determine

To find: The fifth term and $nth$ term of the geometric sequence.

Answer to Problem 17AYU

The fifth term of the geometric sequence is $162$ and the $nth$ term is $a_n=a_1{r}^{n-1}$ .

Explanation of Solution

Given information:

The first term $a_1=2$ and the common ratio $r=3$ .

Calculation:

The formula for nth term of geometric sequence is given by,

  $a_n=a_1{r}^{n-1}$

Calculate the fifth term.

  $\begin{array}{c}{a}_n=\left(2\right){\left(3\right)}^{5-1}\\ =\left(2\right){\left(3\right)}^4\\ =162\end{array}$

Therefore, the fifth term of the geometric sequence is $162$ and the $nth$ term is $a_n=a_1{r}^{n-1}$ .