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The first term of a G.P . Is and the sum...

The first term of a G.P . Is and the sum of `3^(rd)` and `5^(th)` terms is 90 . Find the common ratio of the G.P.

Text Solution

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`a=1,T_(3)+T_(5)=90rArrar^(2)+ar^(4)=90rArrr^(2)+r^(4)=90`
`r^(4)+r^(2)-90=0rArrr^(4)+10r^(2)-9r^(2)-90=0rArrr^(2)(r^(2)+10)-9(r^(2)+10)=0`
`rArr(r^(2)-9)(r^(2)+10)=0rArrr^(2)=-10rArrr=sqrt(-10)` not possible
`r^(2)-9=0rArrr^(2)=9rArrr=+-3`
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