= 6. (4 bonus marks) The sequence of Fibonacci numbers f1, f2,... is recursively defined by fi 1, f2 = 1 and fn = fn−1 + fn-2 for n ≥ 3. If fn is computed by repeatedly applying the defining recurrence, then it is eventually expressed as an f2 + bnf₁ for some integers an and bn. For example, f3 = 1f2+1f1, so a3 = b3 = 1 and f4 = f3+ f2 = 1ƒ2+1ƒ1 + f2 = 2f2+ f1, so a4 2 and 64 = 1. Give a recursive definition of the sequences a3, a4,... and b3, b4,.... What are the numbers an and bn really?