# Consider the sequence -2, -4, -8, -16,... how do you find the 8th term of the sequence?

Apr 14, 2016

-256

#### Explanation:

This is a geometric sequence. The standard sequence being:

a , ar ,$a {r}^{2} , a {r}^{3} , \ldots \ldots \ldots \ldots , a {r}^{n - 1}$

where a represents the 1st term , r , the common ratio and
$a {r}^{n - 1} , \text{ the nth term }$

$a {r}^{n - 1} \text{ is used to find any term in the sequence }$

In this question a = -2 , r =(-4)/(-2) =(-8)/(-4) = 2 " and n = 8

$\Rightarrow {a}_{8} = - 2 \times {\left(2\right)}^{7} = - 2 \times 128 = - 256$