A sequence is defined by the general term

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

Problem

a_n = pn + q

, where

p

and

q

are real constants and

n \ge 1

. (a) Prove that the sequence

\{a_n\}

is an arithmetic progression. (b) Conversely, let

\{b_n\}

be any arithmetic progression with first term

b_1

and common difference

d

. Prove that

b_n

can be expressed in the form

b_n = pn + q

, and identify

p

and

q

in terms of

b_1

and

d