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Question

How many terms of the G.P., 3,32,34..., are needed to give the sum 3069512?

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Solution

Given: G.P. 3,32,34,... and Sn=3069512

Here, first term a=3
common ratio =r=323=12
We know that, sum of n terms of G.P. is given by
Sn=a(1rn)1r
3069512=3[1(12)n]112
3069512×6=[1(12)n]
(12)n=(130693072)
(12)n=(307230693072)
(12)n=(33072)
(12)n=(11024)
(12)n=(12)10

On comparing of powers, we get
n=10
Hence, 10 terms are needed to give the sum 3069512.

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