Having trouble finding the pattern for the language of this DFA:
I can see that anything in the language must start with an a, but after that I cant see how you would generalise all the possible ways to get to the favourable state r. (i.e. abab, aa, aba, aab etc)
In states $q$ and $r$, we can add as many $b$'s as we want. Ignoring the $b$'s, we note that there must be an even number of $a$'s in order to reach state $r$. Hence, the language accepted consist of all strings which start with $a$, and have an even number of $a$'s.