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

1 Answer
Jul 17, 2017

Answer:

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.