# 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 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

sn = $\frac{a(1-r^n)}{1-r}$

The fifth term is given by S5= $\frac{3(1- (0.5)^5)}{1- 0.5}$

= 5.8125.

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

Solution:

Here,

a = 2,

r = 20,

n = 10

The 10th term in the series is given by S10 = $\frac{a(1-r^n)}{1-r} = \frac{2(1-20^{10})}{1-20}$

= $\frac{2(1-20^{10})}{1-20} = \frac{2 \times (-1.024 \times 10^{13})}{-19}$

= $\frac{-2.048 \times 10^{13}}{-19}$ = 1.0778 × 1012.

#### Practise This Question

Which of the following is an adjacent side of AB?