Question

If m times the mth term of an A.P. is equal to n times the nth term, find the
(m + n)th term of the A.P.​

Answer 1

Answer:

nth term of AP =tn =a+(n−1)d

mth term of AP =tm =a+(m−1)d

⇒mtm=ntn

m[a+(m−1)d]=n[a+(n−1)d]

m[a+(m−1)d]−n[a+(n−1)d]=0

a(m−n)+d[(m+n)(m−n)−(m−n)]=0

(m−n)[a+d((m+n)−1)]=0

a+[(m+n)−1]d=0

But tm+n =a+[(m+n)−1]d

∴tm+n =0