Mathematics

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.

Intuitive explanation

The key insight is that in an arithmetic progression, the middle term is always the average of its neighbors. This means if you know $a$ , $b$ , and $c$ are consecutive, you can write a single equation relating them: $b = \frac{a+c}{2}$ , or equivalently $2b = a + c$ . This relationship is your anchor—use it to simplify whatever the problem asks you to prove or find.

Intuitive explanation

Browse the problem library