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.

Question

Philoid · Accepted 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 first pq terms of the A.P. is