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Geometric Series Formula

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

Geometric Series Formula

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

 

Geometric Series Examples

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Lets see some examples on geometric series:

Solved Examples

Question 1: Find the fifth term of geometric series if a = 3, r =0.5.
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 $\times$ 1012.