What sequence is created when the common difference is 0?

1 Answer
Dec 21, 2015

Answer:

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#.