How do you determine whether the sequence $3, 12, 21, 30,...$ is geometric and if it is, what is the common ratio?

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Answer 1 · 2017-07-17T06:44:00

It is not a geometric sequence and hence question of common ratio does not arise. It is actually arithmetic sequence and common difference is $9$ .

A geometric sequence is one in which the ratio of each term to its preceding term is always constant. This ratio is called common ratio.

In the series, ${3,12,21,30,.............}$

we have $12/3=4$ , $21/12=7/4$ , $30/21=10/9$

Hence it is not a geometric sequence.

However, we have $12-3=21-12=30-21=9$ and hence we have a common difference and hence it is an arithmetic sequence.

How do you determine whether the sequence 3, 12, 21, 30,...3, 12, 21, 30,... is geometric and if it is, what is the common ratio?