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

1. 0, 1

2. 0, −1

3. −1, 1

4. −2, 2

We know that,

The numbers are in G.P., if the ratio of consecutive terms are equal.

$\Rightarrow \dfrac{x}{-\dfrac{2}{7}} = \dfrac{-\dfrac{7}{2}}{x} \\[1em] \Rightarrow x^2 = \dfrac{-7}{2} \times \dfrac{-2}{7} \\[1em] \Rightarrow x^2 = \dfrac{14}{14} \\[1em] \Rightarrow x^2 = 1 \\[1em] \Rightarrow x = 1 \text { or } x = -1.$

Hence, option 3 is the correct option.