Question

If m times the mth term of an AP is equal to n times its nth term. Find its (m + n)th term.
OR Prove that its (m + n)th term.
[CBSE 2008, 2012]​

Answer 1

$\huge\pink{\mathbb{ANSWER}}$

Let the first term of AP common difference =d We have to show that (m+n)th term is zero or a + (m+n-1)d = 0

mth term = a + (m-1)d

nth term = a + (n-1) d

Given that m(a +(m-1)d) = n(a + (n -1)d}

- am + m d -md = and - nd

→ am an + m d - nd-md + nd = 0

a(m-n) + (m²-n?)d - (m-n)d = 0

a(m-n) + {(m-n)(m+n)}d -(m-n)d = 0

a(m-n) + {(m-n)(m+n) - (m-n)] d = 0

a(m-n) + (m-n)(m+n-1) d = 0

(m-n){a + (m+n-1)d} = 0

a + (m+n -1)d = 0/(m-n)

a+ (m+n -1)d = 0

Proved!