How to find a term in an arithmetic progression given relationships among the terms? The title is bad, but I was unable to think of better one, I apologize for this. 
I have this system:
\begin{align*}
a_2 + a_3 + a_4 + a_5 & = 34\\
a_2 * a_5 & = 52
\end{align*}
I have to find the $20$th member of the progression ($a_{20}$). Also I know that the progression is growing e.g. $a_1 < a_2 < a_3 \ldots$ 
Any ideas how to solve this task?
I've used the formula $a_n = a_1 + (n-1)d$, but I get an unrealistic equation.

You can set up a system of two equations.  First off, $a_2+a_5=17$ because $a_2+a_5=a_3+a_4$  So your system is $$a_2+a_5=17\\a_2\times a_5=52$$  Do you know how to solve that system?
