The sum of firstthree terms of a G.P. is 16 and the sum of the next th – InterviewSolution

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1.	The sum of firstthree terms of a G.P. is 16 and the sum of the next three terms is 128.Determine the first term, the common ratio and the sum to n terms of the GP.
Answer» Let a be the first term and r be the common ratio of the given GP. Then, `a+ar+ar^(2)=16` and `ar^(3)+ar^(4)+ar^(5)=128` `rArr a(1+r+r^(2))=16` ...(i) and `ar^(3)(1+r+r^(2))=128` ...(ii). On dividing (ii) by (i), we get `r^(3)=8=2^(3) rArr r=2`. Putting `r=2` in (i), we get `a(1+2+4)=16rArr a=16/7`. Thus, in the given GP, we have `a=16/7` and `r=2 gt 1`. `:. S_(n)=(a(r^(n)-1))/((r-1))=(16/7xx(2^(n)-1))/((2-1))=16/7 (2^(n)-1)`.

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