# How do you determine whether the sequence 9, -6, 4, -8/3,... is geometric and if it is, what is the common ratio?

Apr 8, 2017

It is a geometric sequence and common ratio is $- \frac{2}{3}$.

#### Explanation:

To find whether a given sequence is geometric sequence or not, we should divide each term by its preceding term to find ratio between them.

If we get the same ratio, it is a geometric sequence.

Here, we are given the sequence as $\left\{9 , - 6 , 4 , - \frac{8}{3} , \ldots .\right\}$ and

as $\frac{- 6}{9} = - \frac{2}{3}$

$\frac{4}{- 6} = - \frac{2}{3}$ and

$\frac{- \frac{8}{3}}{4} = - \frac{2}{3}$

As ratio is same, it is a geometric sequence and common ratio is $- \frac{2}{3}$.