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

1 Answer
Shwetank Mauria
Jul 17, 2017

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.

Related questions
See all questions in Geometric Sequences
Impact of this question
8375 views around the world
You can reuse this answer
Creative Commons License