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If the sum of n terms of a G.P. is 3(3^(...

If the sum of `n` terms of a G.P. is `3(3^(n+1))/(4^(2n))` , then find the common ratio.

Text Solution

Verified by Experts

`S_(n)=3-(3^(n+1))/(4^(2n))`
Putting n=1,2, we get
`T_(1)=S_(1)=3-9/16=39/16`
`S_(2)=3-27/256=T_(1)+T_(2)`
`rArrT_(2)=S_(2)-T_(1)`
`=(3-27/256)-(3-9/16)=117/256`
`rArrr=(T_(2))/(T_(1))=256/(39/16)`
`(117xx16)/(256xx39)=3/16`
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