Consider the Fibonacci sequence, give a proof by induction to show that 3 | f4n, for all n ≥ 1

I have to show by mathematical induction that 3 | f4n, for all n ≥ 1

Base Case : f4(1) = f4 = 3 which is divisible by 3.

Inductive Hypothesis (IH): Assume 3 | f4k for all k ≥ 1

Inductive step (IS): Show 3 | f4(k+1)

In order to show that 3 | f4(k+1), I said that 3 will always be divisible by f4k as long as k≥1 as we showed in the IH. Hence, (k+1) can be any integer as long as k≥1 and it's a multiple of 4. So, 3 | f4(k+1) will always be true. I don't know how to show this mathematically tho?