Q. 54.4( 142 Votes )

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

Answer :

Let t_{n} = n^{th} tern of AP

t_{n} = a + (n – 1)d

S_{n} = sum of n terms of AP

Let a be the first term and d common difference.

Given, in an AP

p^{th} term = 1/q

………………………………..(I)

q^{th} 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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