Challenge Level

In the Fibonacci sequence each term is the sum of the two terms before it:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

Where do the even numbers come in the sequence?

Is there a pattern? Why?

Which Fibonacci numbers are divisible by 3?

Prove general results for the occurrence of even Fibonacci numbers in the sequence and for the occurrence of multiples of 3.