Question

Find x so that x, x + 2, x + 6 are consecutive terms of a geometric progression.

Answer 1

Given x, x + 2 and x + 6 are in G.P. but read it as x, x + 2 and x + 6. 

∴ r = \(\frac{t_2}{t_1}\) = \(\frac{t_3}{t_2}\)

⇒ \(\frac{x+2}{x}\)= \(\frac{x+6}{x+2}\)

⇒(x + 2)² = x(x + 6) 

⇒ x² + 4x + 4 = x² + 6x 

⇒ 4x – 6x = – 4 = -2x = -4 

∴ x = 2