Insert two number between 3 and 81 so that theresulting sequence is G. – InterviewSolution

InterviewSolution

1.	Insert two number between 3 and 81 so that theresulting sequence is G.P.
Answer» Let the required numbers be `G_(1)` and `G_(2)`. Then, `3, G_(1), G_(2), 81` are in GP. Let the common ratio of this GP be r. Then, `T_(4)=81 rArr ar^((4-1))=81` `rArr 3xxr^(3)=81 rArr r^(3)=27=(3)^(3) rArr r=3`. `:. G_(1)=(3 xx r)(3xx3)=9` and `G_(2)=(3xxr^(2))=(3xx9)=27`. Hence, the required numbers are 3 and 27.

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