Let an AP have first term and common difference

MATHEMATICS · Subjective · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let an AP have first term

a

and common difference

d

, and let a GP have the same first term

a

and common ratio

r\,(r\ne1)

. Derive, in terms of

a,d,r

and

n

, a simplified expression for

S_{AP}-S_{GP}

, where each sum is taken over the first

n

terms.