Q18 of 47 Page 1

If the mth term of an A. P. is and nth term is then show that its (mn)th term is 1.

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


⇒ an – am – nd + md = 0


⇒ 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,


Now, (mn)th terms of AP is


amn = a + (mn – 1)d




⇒ amn = 1


Hence Proved


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