Question

If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero, (p ≠ q)

Answer 1

For an A.P., let a be the first term and d be the common difference. 

The sum of first n terms of an A.P. is given by 

S_n = [2a + (n – 1)d] 

According to the given condition, 

Sp = Sq

∴ The sum of the first (p + q) terms is zero