If m times the mth term of an AP is equal to n times its nth term, find (m+n)th term

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1

If m times the mth term of an AP is equal to n times its nth term, find (m+n)th term.

2

let the first be and common difference is .

Given m times the mth term = n times the nth term

Recall that the nth term of AP is

Similarly, the mth term of AP is

But,

Hence, (m+n)th term of an AP is zero.