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If mth term of an AP is 1/n and its nth ...

If mth term of an AP is 1/n and its nth term is 1/m , then show that its (mn)th term is 1

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If A snd B are constants, then rth term of AP is
`t_(r)=Ar+B`
Given, `t_(m)=(1)/(m) implies Am+B=(1)/(n) " " "…."(i)`
and `t_(n)=(1)/(m) implies An+B=(1)/(m) " " "…."(ii)`
From Eqs. (i) and (ii), we get `A=(1)/(mn)` and B=0
mnth term `=t_(mn)=Amn+B=(1)/(mn).mn+0=1`
Hence, mn term of the given AP is 1.
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Knowledge Check

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