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

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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