# What sequence is created when the common difference is 0?

Dec 21, 2015

A constant sequence.

#### Explanation:

It is an arithmetic sequence and if the initial term is non-zero, then it is also a geometric sequence with common ratio $1$.

This is almost the only kind of sequence that can be both an arithmetic and geometric sequence.

What is the almost?

Consider integer arithmetic modulo $4$. Then the sequence $1$, $3$, $1$, $3$,... is an arithmetic sequence with common difference $2$ and a geometric sequence with common ratio $- 1$.