Question

Find the value of x such that
$-\frac{2}{7},x,-\frac{7}{2}$ are three consecutive terms of a G.P.

Answer 1

Given,

$-\frac{2}{7},x,-\frac{7}{2}$ are in G.P.

Common ratio $r=\frac{x}{-\frac{2}{7}}$...(1)

Common ratio $r=\frac{-\frac{7}{2}}{x}$...(2)

equating (1) and (2), we get,

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

$x^2=(-\frac{7}{2})(-\frac{2}{7})$

$x^2=\pm 1$

$\therefore -\frac{2}{7},1,-\frac{7}{2}$ are in G.P.

$\therefore -\frac{2}{7},-1,-\frac{7}{2}$ are in G.P.