A calculus problem by U Z

Let ${a_{n}}$ be an A.P with common difference d , ${b_{n}}$ be a G.P with common ratio q , where q is appositive rational number . If $b_{1} = d$ $b_{1} = d^{2}$ and $\frac{\sum (a_{1})^{2}}{\sum b_{1}}$ is a positive integer ,then $q = \frac{x}{y}$

x + y=

This question is flagged because it is unclear what $\frac{\sum (a_{1})^{2}}{\sum b_{1}}$ means. Supposedly, it should be indexed, as opposed to the sum of constants.