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.