# If m times the mth term is equal to n times the nth term of an A.P. prove that (m+n)th term of A.P is zero

Arithmetic progression is a series with a common difference in every consecutive term in it.

## Answer: t_{(m+n) }= 0

Gothrough the steps to understand better.

**Explanation:**

Given,

nth term of AP = tn = a + (n − 1)d

mth term of AP = tm = a + (m − 1)d

⇒ mtm = ntn

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

(m − n)[a + d((m + n) − 1)] = 0

a + [(m + n) − 1]d = 0

But tm+n = a + [(m + n) − 1]d

∴tm+n = 0