Question

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

Find$a_{15}$given$a_1=-4$and$r=-3$.

Short answer

The value of$a_{15}$is$-19,131,876$.

Step-by-step solution

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

The given information is:

$a_1=-4$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

$a_1=-4,r=-3$and $n=15$

localid="1645330740894" $$\begin{gathered} a_{15}=(-4){(-3)}^{15-1} \\ =(-4){(-3)}^{14} \\ =(-4)\left(4782969\right) \\ =-19,131,876 \end{gathered}$$

$a_{15}=-19,131,876$