For what values of $x$, the numbers $\frac{2}{7}, x,-\frac{7}{2}$ are in $G.P.$?
For what values of $x$, the numbers $\frac{2}{7}, x,-\frac{7}{2}$ are in $G.P.$?
The given numbers are $\frac{-2}{7}, x, \frac{-7}{2}$
Common ratio $=\frac{x}{-2 / 7}=\frac{-7 x}{2}$
Also, common ratio $=\frac{-7 / 2}{x}=\frac{-7}{2 x}$
$\therefore \frac{-7 x}{2}=\frac{-7}{2 x}$
$\Rightarrow x^{2}=\frac{-2 \times 7}{-2 \times 7}=1$
$\Rightarrow x=\sqrt{1}$
$\Rightarrow x=\pm 1$
Thus, for $x=\pm 1,$ the given numbers will be in $G.P.$
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