How do you tell whether the sequence 1, 3, 7, 15, 31,... is geometric?

1 Answer
Mar 5, 2017

It is not, since it has no common ratio.

Explanation:

This sequence is not geometric as the ratio between successive pairs of terms is not constant. For example:

3/1 = 9/3 != 7/3

Adding 1 to each element does result in a geometric sequence:

2, 4, 8, 16, 32,...

(with common ratio 2) and hence we can write a formula for the nth term of our original sequence:

a_n = 2^n-1