Question

If n times the nth term is equal to m times of mth term then m+n =

Answer 1

ANSWER

m×am=n×an

m{a+(m−1)d}=n{a+(n−1)d}

am+m2d−md=an+n2d−nd

am−an=−m2d+n2d−nd+md

a(m−n)=d(n2−m2+m−n)

a(m−n)=d{(n−m)(n+m)+m−n}

a(m−n)=d(m−n){−1(n+m)+1}

a=d(−n−m+1)...(1)

To prove: (m+n)th term is zero

(m+n)thterm=a+(n−1)d

here, n= number of terms

=a+(m+n−1)d=0...(2)

Substituting a=d(−n−m+1) in (2)

=d(−n−m+1)+(m+n−1)d

=−dn−dm+d+md+nd−