# Determine whether the sequence 9,−6,4,−8/3,... is geometric and if it is, what is the common ratio

Determine whether the sequence $9,-6,4,-\frac{8}{3},...$ is geometric and if it is, what is the common ratio
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

domwaheights0m
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 $\left\{9,-6,4,-\frac{8}{3},....\right\}$ 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 $-\frac{2}{3}$.