Question

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

Answer 1

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`.

Explanation:

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.