Question

If the sum of the first p terms of an A.P. is q and the sum of first q terms is p, then find the sum of first (p + q) terms.

Answer 1

Given: S_p = q and S_q = p

To find: S_p+q

We know that,

Now,

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

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

⇒ S_p+q = - (p+q)

Hence, the sum of first (p + q) terms is –(p + q)