Question

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

Answer 1

G.P. = x + 6, x + 12, x + 15

In G.P. r = `("t"_2)/("t"_1) = ("t"_3)/("t"_2)`

`(x + 12)/(x + 6) = (x + 15)/(x + 12)`

(x + 12)² = (x + 6) (x + 15)

x² + 24x + 144 = x² + 6x + 15x + 90

24x – 21x = 90 – 144

3x = – 54

x = `(-54)/3` = – 18

x = – 18