I've moved this to Algebra. It's a good idea to let us know why you're stuck, especially when a hint has already been provided. For example, did you understand the wording of the problem? Do you know that "sequence" and "series" have different meanings?
Each term in the sequence is the average of two positive terms, and is therefore positive. Does that matter?
Using the hint given, and multiplying both sides by $2a$ (to clear both fractions), gives $2a^2 = a^2 + 2$, which implies $a^2 = 2$. Now what?