Q29 of 47 Page 1

If the pth term of an A. P. is and qthterm is prove that the sum of first pq terms of the A. P. is

Given:


Now, ap = a + (p – 1)d



⇒ aq + q(p – 1)d = 1


⇒ aq + pqd – qd = 1 …(i)




⇒ ap + pqd – pd = 1 …(ii)


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


aq + pqd – qd = ap + pqd – pd


⇒ aq – ap – qd + pd = 0


⇒ a(q – p) – d (q – p) = 0


⇒(q – p)[a – d] = 0


⇒ a = d


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


dq + pqd – qd = 1


⇒ pqd = 1



Hence,


Now, we have to show that sum of first pq term is


We know that,



For sum of first pq terms,


Putting n = pq,





Thus, sum of first pq terms is


Hence Proved


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