Question

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

Find$a_{10}$givenrole="math" localid="1645328421912" $a_1=-6$and$r=-2$.

Short answer

The value of$a_{10}$is$3,072$.

Step-by-step solution

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

The given information is:

$a_1=-6$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

$a_1=-6,r=-2$and $n=10$

localid="1645330542045" $$\begin{gathered} a_{10}=(-6){(-2)}^{10-1} \\ =(-6){(-2)}^9=(-6)(-512) \\ =3,072 \end{gathered}$$

$a_{10}=3,072$