Q. 54.4( 142 Votes )

In an A.P., if pth term is 1/9 and qth term is1/p, prove that the sum of first pq terms is 1/2 (pq +1), where p 1/7 q.

Answer :

Let tn = nth tern of AP


tn = a + (n – 1)d


Sn = sum of n terms of AP



Let a be the first term and d common difference.


Given, in an AP


pth term = 1/q


………………………………..(I)


qth term = 1/p


………………………………(II)


(I) – (II)





Putting value of d in (I)








Thus, the sum of the first pq terms of the A.P. is .

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