Geometric Series Formula

The Geometric series formula or the geometric sequence formula gives the sum of a finite geometric sequence. The geometric series is that series formed when each term is multiplied by the previous term present in the series. The sequence will be of the form {a, ar, ar², ar³, …….}.

Geometric Series Formula

The geometric series formula is given by

Here a will be the first term and r is the common ratio for all the terms, n is the number of terms.

Solved Example Questions Based on Geometric Series

Let us see some examples on geometric series.

Question 1: Find the sum of geometric series if a = 3, r = 0.5 and n = 5.

Solution:

Given:

a = 3

r = 0.5

n = 5

s_n =

The sum of five terms is given by S₅=

= 5.8125

Question 2: Find S₁₀ if the series is 2, 40, 800,…..

Solution:

From the given,

a = 2

r = 20

n = 10

The 10th term in the series is given by S₁₀ =

=

=