How many terms of the GP `3,3/2,3/4,......` are needed to give sum `30 – InterviewSolution

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1.	How many terms of the GP `3,3/2,3/4,......` are needed to give sum `3069/512`?
Answer» series in GP=`a, ar, ar^2, ar^3, ....., ar^(n-1)` `= a(1-r^n)/(1-r)` where `a=3 ; r=1/2` `S_n = (3(1-1/2^n))/(1-1/2)` `6(1-1/2^n) = 3069/512` `1-1/2^n = (510+9/6)/512` `1 -1/2^n = 1- 3/(6 xx 512)` `1/2^n = 1/(512 xx 2) = 1/(2^9 xx 2)` `n=10` answer

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