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#.