Question

If in an A.P„ sum of p terms is equal to sum of q terms, then find the sum of (p + q) terms.

Answer 1

Let a₁ is the first term and d is the common difference of A.P.

Then, sum of first p terms

S_p = p/2[2a₁ + (p - 1)d]

and sum of first q terms

Sq = q/2[2a₁ + (q - 1)d]

According to question,

some of first p terms = sum of first q terms

Now, sum of (p + q) terms of this progression

Hence, sum of (p + q) terms of given A.P. is zero.