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

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Answer 1 · 2017-04-08T04:07:12

It is a geometric sequence and common ratio is $-2/3$ .

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 ${9,-6,4,-8/3,.... }$ and

as $(-6)/9=-2/3$

$4/(-6)=-2/3$ and

$(-8/3)/4=-2/3$

As ratio is same, it is a geometric sequence and common ratio is $-2/3$ .

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