Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression.

Solution :

b = √ac

(x + 12) = √(x + 6) (x + 15)

Taking squares on both sides,

(x + 12)2 = (x + 6) (x + 15)

x2 + 122 + 2x(12) = x2 + 15x + 6x + 90

144 + 24x = 21x + 90

24x - 21x = 90 - 144

3x = -54

x = -18

Hence the value of x is -18.