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Question

Find the sum to n terms of a G.P. 7,21,37...

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Solution

Given, 7,21,37...
First term =a=7 and
Common ratio =r=217=7×37=3>1

We know, the sum of n terms of G.P. is
Sn=a(rn1)r1
Sn=7(3n1)31
By using rationalization,
Sn=7((3)n1)31×3+13+1

Sn=7(3)n2131×(3+1)

Sn=7(3)n212×(3+1)

Sn=7(3+1)(3)n212

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