What is the sum of the first seven terms of the geometric series?
3 + 12 + 48 + 192 + …

Solution:

Given a Geometric series 3 + 12 + 48 + 192 + …

The first term a = 3

The common ratio r = 12/3 = 48/12 = 192/48 = 4

We observe that r > 1. 

If r > 1, the sum of a GP of the first n terms is given by S\(_n \)= a(rⁿ - 1)/(r-1)

Plugginig in the values a = 3, n =7 and r = 4, then we have

S\(_n \) = 3(4⁷ - 1)/(4 - 1)

= 3(4⁷ - 1)/3

= (4⁷ - 1) = 16384 - 1

= 16383

What is the sum of the first seven terms of the geometric series?
3 + 12 + 48 + 192 + …

Summary:

The sum of the first seven terms of the given GP series is 16383.