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 number of terms.
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Geometric Series Examples
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:
Solution:
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Given : a = 3, r = 0.5, n = 5
Given : a = 3, r = 0.5, n = 5
sn = $\frac{a(1-r^n)}{1-r}$
The fifth term is given byÂ
S5=Â $\frac{3(1- (0.5)^5)}{1- 0.5}$
   = 5.8125.
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Question 2: Find S10 if the series is 2, 40, 800,…..
Solution:
Solution:
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Here a = 2, r = 20, n = 10
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.
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