What sequence is created when the common difference is 0?

1 Answer
George C.
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.

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