Question

if n times the nth term of an AP is equal to m times the mth term of AP then prove that (m+n)th term is equal to zero.

Answer 1

Tn=a+(n-1)d

Tm=a+(m-1)d

Also,n.Tn=m.Tm

=>n[a+(n-1)d]=m[a+(m-1)d]

=>an+n^2 d-nd=am+m^2 d-md

=>a(n-m)+(m-n)d+(n^2-m^2)d=0.

=>a(n-m)+d[(n+m)(n-m)-(n-m)]=0

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

=>(n-m)[a+(m+n-1)d]=0

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

=>T(m+n)=0

Hope it helps

Answer 2

hope you get help from this