Question

if m times mth term of an A.P. is equal to the n times nth term, then show that (m+n)th term of the A.P. is zero.

Answer 1

I..hope..it..help..you...

Answer 2

Hey dear,

◆ Proof -
Consider an AP with a as first term and d as common difference.

Given is-
m(tm) = n(tn)
m[a+(m-1)d] = n[a+(n-1)d]
ma + dm^2 - md = na + dn^2 - nd
ma-na + dm^2 - dn^2 - md + nd
a(m-n) + d(m+n)(m-n) - d(m-n) = 0

Dividing whole eqn by (m-n),
a + d(m+n) - d = 0
a + (m+n-1)d = 0

But we know,
a + (m+n-1)d = (m+n)th term

Therefore
(m+n)th term = 0

Hope it helps...