Find a, b and c such that the following numbers are in AP, a, 7, b, 23 and c.

Given: a, 7, b, 23 and c are in AP.

To find: a, b and c

Formula Used:

d = a₂ – a₁ = a₃ – a₁ = __________ for n terms

Explanation:

For the above terms to be in AP.’

The difference of successive terms should be equal

i.e

a₅ - a₄ = a₄ - a₃ = a₃ - a₂ = a₂ - a₁ = d

where d let be common difference

7 - a = b - 7 = 23 - b = c - 23

Implies b - 7 = 23 - b

2b = 30

b = 15 ( eqn 1 )

Also

7 - a = b - 7

from eqn 1

7 - a = 15 - 7

a = - 1

and

c - 23 = 23 - b

c - 23 = 23 - 15

c - 23 = 8

c = 31

so a = - 1

b = 15

c = 31

and the sequence - 1, 7, 15, 23, 31 is an AP