jmc

Let the common ratio of the geometric sequence be $r$. We have the equations $20\cdot r=a$ and $a\cdot r=\frac{5}{4}$. In the first equation, we solve for $r$ to get $r=\frac{a}{20}$, and substitute this into the second equation to eliminate $r$, resulting in $a\cdot \frac{a}{20}=\frac{5}{4}$, or $a=\boxed{5}$.