Insert threenumbers between 1 and 256 so that the resulting sequence i – InterviewSolution

InterviewSolution

1.	Insert threenumbers between 1 and 256 so that the resulting sequence is a G.P.
Answer» Let the required numbers be `G_(1), G_(2), G_(3)`. Then, `1, G_(1), G_(2), G_(3), 256` are in GP. Let r be the common ratio of this GP. Then, `T_(5)=256 rArr ar^((5-1))=256` `rArr 1xxr^(4)=256 rArr r^(4) =256= (4)^(4) rArr r=4`. `:. G_(1)=(1xx4)=4, G_(2)=(1xx4^(2))=16` and `G_(3)=(1xx4^(3))=64`. Hence, the required are 4, 16, 64.

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