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

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