If `m` times the `m^(t h)` term of an A.P. is equal to `n` times its `n^(t h)` term, show that the `(m+n)^(t h)` term of the A.P. is zero.

Explanation

Given,


nth term of AP =`t _n​` `=a+(n−1)d`

mth term of AP =`t _m` `=a+(m−1)d`

⇒`mt_m` =`nt_n`

`m[a+(m−1)d]=n[a+(n−1)d]`

`m[a+(m−1)d]−n[a+(n−1)d]=0`

`a(m−n)+d[(m+n)(m−n)−(m−n)]=0`
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