Question

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

Find$a_{11}$given$a_1=8$and$r=3$.

Short answer

The value of$a_{11}$is role="math" localid="1645271579494" $472,392$.

Step-by-step solution

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

The given information is:

$a_1=8$and$r=3$

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

$a_1=8,r=3$and $n=11$

localid="1645272567640" $$\begin{gathered} a_{11}=\left(8\right){\left(3\right)}^{11-1} \\ =\left(8\right){\left(3\right)}^{10} \\ =\left(8\right)\left(59049\right) \\ =472,392 \end{gathered}$$

$a_{11}=472,392$