Arithmetically correct

Algebra Level 4

Let $${ T }_{ r }$$ be the $${ r }^{\text{ th} }$$ term of an arithmetic progression. for $$r = 1,2,3, \ldots$$. If for some positive integers $$m, n$$, we have $${ T }_{ m }=\frac { 1 }{ n }$$, $${ T }_{ n }=\frac { 1 }{ m }$$, then $${ T }_{ mn }$$ equals to?

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