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The 4^(th) and 9^(th) terms of a G.P. A...

The `4^(th)` and `9^(th)` terms of a G.P. Are 54 and 13122 respectively .Find the `6^(th)` term .

Text Solution

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`T_(4)=54rArrar^(3)=54`
`T_(9)=13122rArrar^(8)=13122`
`therefore(ar^(8))/(ar^(3))=(13122)/(54)rArrr^(5)=243rArrr^(5)rArrr=3`
`ar^(3)=54rArra.3^(3)=54rArra.27=54rArra=2`
`T_(6)=ar^(5)=2.3^(5)=2xx243=486`
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