Q76 of 84 Page 5

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. (CBSE 2015)

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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