Challenge Level

You may have seen this sequence before: $$1, 1, 2, 3, 5, 8, 13, 21, ... $$

It is called the Fibonacci Sequence, and each term is calculated by adding together the previous two terms in the sequence.

Try adding together any three consecutive Fibonacci numbers.

Can you explain it?

Choose any four consecutive Fibonacci numbers. Add the first and last, and divide by two.

Can you explain it?

Add together any six consecutive Fibonacci numbers and divide by four.

Can you explain it?

Can you discover any Fibonacci Surprises of your own?