If $\frac{1}{5}:\frac{1}{x}=\frac{1}{x}:\frac{1}{1.25}$ , then the value of x is 

Given $\frac{1}{5}:\frac{1}{x}=\frac{1}{x}:\frac{1}{1.25}$

Use the ratio

$\begin{array}{rcl}\frac{1}{5}·\frac{x}{1}& =& \frac{1}{x}·\frac{1.25}{1}\\ \frac{x}{5}& =& \frac{1.25}{x}\end{array}$

cross multiply 

$\begin{array}{rcl}{x}^2& =& 5\left(1.25\right)\\ & =& 6.25\end{array}$

Apply square root on both sides 

$\begin{array}{rcl}x& =& \sqrt{6.25}\\ & =& \boxed{\mathbf{2}\mathbf{.}\mathbf{5}}\end{array}$