The first, the third and the fifth term of a GP are the first, the second and the sixth term of an AP, respectively. Find the common ratio of the GP.
Let $a_1, a_2=a_1q, a_3=a_1q^2...$ be in G.P. and $b_1, b_2=b_1+d,...$ be in AP.
I tried to solve the system $$\begin{cases}a_1=b_1\\a_3=a_1q^2=b_2=b_1+d\\a_5=a_1q^4=b_6=b_1+5d\end{cases}$$ and from here to solve for the common ratio, but I wasn't able to. Thank you in advance!