# How do you find the missing term in the geometric sequence: -5, 10, -20, 40, __?

Oct 31, 2016

$- 80$

#### Explanation:

The standard $\textcolor{b l u e}{\text{geometric sequence}}$ is.

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

where r is the common ratio.

and $r = {a}_{2} / {a}_{1} = {a}_{3} / {a}_{2} = \ldots \ldots . . = {a}_{n} / \left(a {r}_{n - 1}\right)$

here $r = \frac{10}{- 5} = \frac{- 20}{10} = - 2$

Hence to find the missing term, multiply the previous term by r.

$\Rightarrow {a}_{5} = - 2 \times 40 = - 80$