Question

For what values of x, the numbers $\frac{-2}{7}$, x , $\frac{-7}{2}$ are in G.P.?

Answer 1

The given numbers are : $\frac{-2}{7}$ , x , $\frac{-7}{2}$

Common ratio =$\frac{x}{\frac{-2}{7}}$ = $\frac{-7x}{2}$

Also, common ratio = $\frac{-7}{\frac{2}{x}}$ = $\frac{-7}{2x}$

∴ -$\frac{7x}{2}$ = $\frac{-7}{2x}$

⇒ $x^2$ = -2 ×$\frac{7}{-2}$ × 7 = 1

⇒ x = $\sqrt{1}$

⇒ x = ±1

Thus, for x = ± 1, the given numbers will be in G.P.