Question

In Problems 31–38, find the nth term $a_n$of each geometric sequence. When given, r is the common ratio.

$a_2=7;r=\frac{1}{3}$

Short answer

The$a_1$term is 21 and$a_n=21·{\frac{1}{3}}^{n-1}$

Step-by-step solution

Step 1. Write the given information.

Given common ratio is$r=\frac{1}{3}and{a}_2=7$

Step 2. 

The formula for the nth term is$a_n=a_1·r^{n-1}$

$$\begin{gathered} a_2=a_1=a·{\frac{1}{3}}^{2-1} \\ 7=a_1·\frac{1}{3} \\ {a}_1=21 \end{gathered}$$

$a_n=21·{\frac{1}{3}}^{n-1}$