$-\dfrac{5}{3}, x \text{ and } -\dfrac{3}{5}$ are three consecutive terms of a G.P. Find the value(s) of x.

Given,

$-\dfrac{5}{3}, x \text{ and } -\dfrac{3}{5}$ are three consecutive terms of a G.P.

$\therefore \dfrac{x}{-\dfrac{5}{3}} = \dfrac{-\dfrac{3}{5}}{x} \\[1em] \Rightarrow x^2= -\dfrac{3}{5} \times -\dfrac{5}{3} \\[1em] \Rightarrow x^2 = 1 \\[1em] \Rightarrow x = \sqrt{1} = \pm 1.$

Hence, x = +1 or -1.