Fibonacci sequence

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?

What have Fibonacci numbers got to do with Pythagorean triples?

Investigate the different ways you could split up these rooms so that you have double the number.

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.