Let the sums of the first and first terms of an arithmetic progression be equal

MATHEMATICS · Multi-part · CBSE · Mathematics · Arithmetic Progressions · Arithmetic Progressions

Problem

Let the sums of the first

p

and first

q

terms of an arithmetic progression be equal, where

p < q

. (i) Establish the relationship between

p

q

and the common difference

d

that is implied by the condition

S_p = S_q

. (ii) Prove that the sum of the next

(q - p)

terms is zero. (iii) If

p = 5

and

q = 8

, find the first term of the AP in terms of

d

, and hence obtain its numerical value when

d = 3