Sum of First n Terms of GP


 
 
Concept Explanation
 

Sum of N Term of a GP

The sum of n terms of a GP with r < 1 is

      frac{a(1-r^n)}{1-r}.

The sum of n terms of a GP with r >  1 is

       frac{a(r^n-1)}{r-1}.

The sum of an infinite number of terms of a decreasing GP is

          = frac{a}{1-r}.

Illustration 1. Find the sum of 5 terms of the series

    frac{1}{5},frac{1}{2},frac{5}{4},....

A. 12.11         B. 12.24        C. 12.88         D. 12.92

Answer: C

Solution The given series is a GP with

 a= frac{1}{5}   

r=frac{5}{2}

Since r > 1, 

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