Start Free Trial

Geometric Sequence. How to check if a given  sum  represents the sum of the terms of a geometric sequence?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The sum of n terms of a geometric sequence is given as a*(r^n - 1)/(r - 1), where r is the common ratio and a is the first term

4^n - 1

=> (2^(2n) - 1) / (2 - 1)

Here a = 1 and r = 2. But 2n can only take on even values.

The expression 4^n - 1 can be the sum of terms of a geometric sequence but it holds only when the number of terms is even.

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team