Let two arithmetic progressions be defined as follows: AP : first term and common…

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let two arithmetic progressions be defined as follows: AP

P

: first term

p

and common difference

d

. AP

Q

: first term

q

and the same common difference

d

(p \ne q,\; d \ne 0)

. Prove that the sums of the first

n

terms of the two progressions can never be equal for any positive integer

n