Question

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

$a_6=243;r=-3$

Short answer

The$a_{1}is-1and{a}_n=-1·{(-3)}^{n-1}$

Step-by-step solution

Step 1. Write the given information

The common ratio is$r=-3and{a}_6=243$

Step 2. Find the a1 and nth term.

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

localid="1646971157096" $$\begin{gathered} a_6=a_1·{(-3)}^{6-1} \\ 243=a_1·{(-3)}^5 \\ 243=a_1·{(-3)}^5 \\ {a}_1=-1 \end{gathered}$$

localid="1646971172213" $$\begin{gathered} a_n=-1·{(-3)}^{n-1} \\ =-1·{(-3)}^{n-1} \end{gathered}$$