Determine whether the sequence $9,-6,4,-\frac{8}{3},...$ is geometric and if it is, what is the common ratio

Marilyn Cameron
2022-10-13
Answered

Determine whether the sequence $9,-6,4,-\frac{8}{3},...$ is geometric and if it is, what is the common ratio

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domwaheights0m

Answered 2022-10-14
Author has **11** answers

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

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

Here, we are given the sequence as $\{9,-6,4,-\frac{8}{3},....\}$ 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 $-\frac{2}{3}$.

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