Q. 36

If the mth term of an A.P. is and the nth term is , then prove that the sum to mn terms is , where in m n.

Answer :

Given:


Now, am = a + (m – 1)d



an + n(m – 1)d = 1


an + mnd – nd = 1 …(i)




am + mnd – md = 1 …(ii)


From eq. (i) and (ii), we get


an + mnd – nd = am + mnd – md


a(n – m) –d (n – m) = 0


a = d


Now, putting the value of a in eq. (i), we get


dn + mnd – nd = 1


mnd = 1



Hence,


Sum of mn terms of AP is







Hence Proved


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