Question

Find the indicated term of each geometric sequence.

$10th$term of$-1,2,-4,......$

Short answer

The$10th$term is$512$.

Step-by-step solution

Step 1. Given information.   

We have, $-1,2,-4,.....$

$a_1=-1,a_2=2,a_3=-4$

The common ratio is

$$\begin{gathered} \frac{a_2}{a_1}=\frac{2}{-1}=-2 \\ \frac{a_3}{a_2}=\frac{-4}{2}=-2 \end{gathered}$$

The common ratio$r=-2$

To find the 10th term.

The $nth$term of a geometric sequence is determined by formula $a_n=a_1{r}^{n-1}$

Substitute $a_1=-1,r=-2$and $n=10$

role="math" localid="1647019188211" $$\begin{gathered} a_n=a_1{r}^{10-1} \\ {a}_{10}=(-1){(-2)}^9 \\ {a}_{10}=512 \end{gathered}$$