Use induction to prove the following a Let fn denote the Fib

Use induction to prove the following.

(a) Let {f_n} denote the Fibonacci sequence. Show f_3n is even and both f_3n+1 and f_3n+2 are odd

for all natural numbers n.

(b) Prove 10ⁿ⁺¹ + 3 · 4ⁿ¹ + 5 is divisible by 9 for all natural numbers n.

Solution

Let {fn} denote the Fibonacci sequence. Show f3n is even and both f3n+1 and f3n+2 are odd

for all natural numbers n.