Fibonacci sequence

There are 31 NRICH Mathematical resources connected to Fibonacci sequence
Stringing it Out
problem

Stringing it out

Age
14 to 16
Challenge level
filled star empty star empty star
Explore the transformations and comment on what you find.
Last Biscuit
game

Last biscuit

Can you find a strategy that ensures you get to take the last biscuit in this game?

Ordered Sums
problem

Ordered sums

Age
14 to 16
Challenge level
filled star filled star empty star
Let a(n) be the number of ways of expressing the integer n as an ordered sum of 1's and 2's. Let b(n) be the number of ways of expressing n as an ordered sum of integers greater than 1. (i) Calculate a(n) and b(n) for n<8. What do you notice about these sequences? (ii) Find a relation between a(p) and b(q). (iii) Prove your conjectures.
Fibonacci Factors
problem

Fibonacci factors

Age
16 to 18
Challenge level
filled star empty star empty star
For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?
Golden Mathematics
article

Golden mathematics

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.