Question

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

$a_1=0,r=\frac{1}{2}$

Short answer

The$nth$term is$a_n=0$and the fifth term is$a_5=0$

Step-by-step solution

Step 1. Given information. 

We have, $a_1=0$and $r=\frac{1}{2}$

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 nth term. 

Substitute $a_1=0,r=\frac{1}{2}$and $n=5$

role="math" localid="1646986476506" $$\begin{gathered} a_n=0{\left(\frac{1}{2}\right)}^{n-1} \\ {a}_n=0 \end{gathered}$$

and

$$\begin{gathered} a_5=0{\left\{\frac{1}{2}\right\}}^{5-1} \\ {a}_5=0{\left\{\frac{1}{2}\right\}}^4 \\ {a}_5=0 \end{gathered}$$