Question 136
Let $\{a_n\}$ be an arithmetic progression with common difference $d$ ($d \neq 0$) and $\{b_n\}$ be a geometric progression with common ratio $q$, where $q$ is a positive rational number less than $1$. If $a_1 = d$, $b_1 = d^2$ and $\frac{a_1^2 + a_2^2 + a_3^2}{b_1 + b_2 + b_3}$ is a positive integer, then $q$ equals ______.