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Let Tr denote the rth term of a G.P. for...

Let `T_r` denote the rth term of a G.P. for `r=1,2,3,` If for some positive integers `ma n dn ,` we have `T_m=1//n^2` and `T_n=1//m^2` , then find the value of `T_(m+n//2.)`

Text Solution

Verified by Experts

The correct Answer is:
1/mn
Given that
`T_(m)=AR^(m-1)=1/n^(2)andT_(n)=AR^(n-1)=1/m^(2)`
`rArrA^(2)R^(m+n-2)=1/(m^(2)n^(2))`
`rArrAR^((m+n)/2-1)=1/(mn)`
`rArrT_((m+n)/2)=1/(mn)`
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