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

1 Answer
Mar 5, 2017

Answer:

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 #n#th term of our original sequence:

#a_n = 2^n-1#