Question

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

$a_1=6,r=-2$

Short answer

The $nth$term is localid="1646985535068" $6{(-1)}^{n-1}$and the fifth term islocalid="1646985543934" $a_5=6$.

Step-by-step solution

Step 1. Given information. 

We have, $a_1=6$and $r=-2$

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

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

Substitute $a_1=6,r=-2$and $n=5$

role="math" localid="1646985361633" $a_n=6{(-1)}^{n-1}$

and

role="math" localid="1646985464675" $$\begin{gathered} a_5=6{(-1)}^{5-1} \\ {a}_5=6{(-1)}^4 \\ {a}_5=6 \end{gathered}$$