Question

If m times the m th term of an AP is equal ton times n th term then show that (m+n)th term of the AP is zero

Answer 1

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

ma+m(m-1)d=na+n(n-1)d

ma+m(m-1)d - na -n(n-1)d=0

a(m-n) +d(msquare-m-nsquare +n) =0

a(m-n) +d(msquare-nsquare -(m-n)) =0

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

m is not equal to n

a+(m+n) d=0

(m+n)th term is zero