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

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

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

Answer»

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