Question

Find the fifth term and the nth term of the geometric sequence whose initial term $a_1$and common ratio $r$are given. $a_1=2,r=3$

Short answer

The$nth$term is$a_n=2\times 3^{n-1}$and the fifth term is$a_5=162$.

Step-by-step solution

Step 1. Given information.

We have$a_1=2$and$r=3$

The $nth$term of a geometric sequence is determined by formula $a_n=a_1{r}^{n-1}$.$a_1=2$

Step 2. To find the fifth term and the nth term.

Substitute $a_1=2,r=3$and $n=5$.

$a_n=2\times 3^{n-1}$

and

$$\begin{gathered} a_5=2\times 3^{5-1} \\ {a}_5=2\times 3^4 \\ {a}_5=162 \end{gathered}$$

The$nth$term is$a_n=2\times 3^{n-1}$and the fifth term is$a_5=162$.