Question

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

Answer 1

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

Common ratio $\left(r_1\right)=\frac{Second}{first}=\frac{x}{\frac{-2}{7}}=\frac{7x}{-2}-----\left(1\right)$

Common ratio $\left(r_2\right)=\frac{Third}{Second}=\frac{\frac{-7}{2}}{x}=\frac{-7}{2x}----\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

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

$7x\left(2x\right)=-7(-2)$

$14x^2=14$

$x^2=1$

$x=\pm 1$

So $x=1$ $x=-1$

$\frac{-2}{7},1,\frac{-7}{2}$ $\frac{-2}{7},-1,\frac{-7}{2}$

$\therefore$ values of $x$ is $1$ & $-1$