Define Fibonacci sequence $\{F\}_{n=0}^{\infty}$ as $F_0 = 0, F_1 = 1$ and $F_{n+1} = F_n +F_{n-1}$ for every integer $n > 1$. Determine all quadruples $(a, b, c,n)$ of positive integers with a $< b < c$ such that each of $a, b,c,a + n, b + n,c + 2n$ is a term of the Fibonacci sequence.