Is 3, 6, 9, 12 ,15, 18 a geometric sequence?

Dec 16, 2015

No, it's an arithmetic sequence with initial term $3$ and common difference $3$.

Explanation:

A geometric sequence has a common ratio between terms.

An arithmetic sequence has a common difference between terms.

If a sequence of Real numbers is both a geometric sequence and an arithmetic sequence then it is constant.

Note I say Real numbers. The sequence $1 , - 1 , 1 , - 1 , \ldots$ is both an arithmetic and geometric sequence in modulo $4$ arithmetic, with common difference $2$ and common ratio $- 1$.