Sequence 1

Let $a,b,c,d$ be 4 positive real numbers with $a<b<c<d$ . Given that $a,b,c,d$ are first 4 terms of an AP and $a,b,d$ are in GP.

The value of $\dfrac{ad}{bc}$ is $\dfrac{p}{q}$ , where $p$ and $q$ are prime numbers.

Find the value of $q$ .