Fibonacci sequence

There are 31 NRICH Mathematical resources connected to Fibonacci sequence
Fibonacci Surprises
problem
Favourite

Fibonacci Surprises

Age
11 to 14
Challenge level
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Play around with the Fibonacci sequence and discover some surprising results!

Fibs
problem
Favourite

Fibs

Age
11 to 14
Challenge level
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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?
1 Step 2 Step
problem
Favourite

1 Step 2 Step

Age
11 to 14
Challenge level
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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?
Golden Fibs
problem

Golden Fibs

Age
16 to 18
Challenge level
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When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!
Sheep Talk
problem

Sheep Talk

Age
7 to 11
Challenge level
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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?
Golden Fractions
problem

Golden Fractions

Age
16 to 18
Challenge level
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Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.
Fibonacci Fashion
problem

Fibonacci Fashion

Age
16 to 18
Challenge level
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What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?
Pythagorean Fibs
problem

Pythagorean Fibs

Age
16 to 18
Challenge level
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What have Fibonacci numbers got to do with Pythagorean triples?
Room Doubling
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Room Doubling

Age
7 to 11
Challenge level
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Investigate the different ways you could split up these rooms so that you have double the number.
Plus or Minus
problem

Plus or Minus

Age
16 to 18
Challenge level
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Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.