KMO 2013 Problem 4

$\{a_n\}$ is a positive integer sequence such that $a_{i+2} = a_{i+1} + a_{i} (i \ge 1)$ . For positive integer $n$ , define $\{b_n\}$ as $$b_n = \frac{1}{a_{2n+1}} \sum_{i=1}^{4n-2} { a_i }$$ Prove that $b_n$ is positive integer, and find the general form of $b_n$ .