Question

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.

Find$a_{13}$given$a_1=7$and$r=2$.

Short answer

The value of$a_{13}$is$28,672$.

Step-by-step solution

Step 1. Write the given information and use the formula of general term

The given information is:

$a_1=7$and$r=2$

The general term of a geometric sequence with the first term $a_1$and the common ratio $r$is:

$a_n=a_1{r}^{n-1}$

Step 2. Substitute the given values into the formula

$a_1=7,r=2$and $n=13$
localid="1645273060798" $$\begin{gathered} a_{13}=\left(7\right){\left(2\right)}^{13-1} \\ =\left(7\right){\left(2\right)}^{12} \\ =\left(7\right)\left(4096\right) \\ =28,672 \end{gathered}$$

$a_{13}=28,672$