Let and be three consecutive terms of an arithmetic progression.

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

Problem

Let

a, b

and

c

be three consecutive terms of an arithmetic progression. (a) Prove that

2b = a + c

. (b) Using the result of part (i), determine whether the numbers

3, 7, 12

can be consecutive terms of an arithmetic progression. Give reasons for your answer. (c) If

p - 4, 2p + 1

and

5p - 9

are consecutive terms of an arithmetic progression, find the value of

p

and write the three terms in increasing order.