# 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

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

(with common ratio

#a_n = 2^n-1#