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Edexcel GCSE Maths Fibonacci sequences

Fibonacci sequences

This page covers the following topics:

1. Basics of Fibonacci sequences
2. Terms in a Fibonacci sequence
3. nth term of Fibonacci sequences

The Fibonacci sequence is 1, 1, 2, 3, … The first 2 terms are 1 and 1, and then to get each next term we add the previous 2 terms together - hence giving a 3rd term: 1 + 1 = 2, and 4th term: 1 + 2 = 3 etc. Choosing different values for the first 2 terms, but following the rule of adding the 2 previous terms to get the next term, gives different Fibonacci-type sequences. Also, note that by positioning squares together where each square's length corresponds to a Fibonacci number, one can draw a spiral through the squares as shown. This is the Fibonacci Spiral, which is a very significant pattern that appears in nature.

Basics of Fibonacci sequences

To get the next term of the Fibonacci sequence (or any Fibonacci-type sequence) one needs to add the previous 2 terms together. To find the term at a specific position in the Fibonacci sequence, one needs to know the previous 2 numbers in the Fibonacci sequence - which in turn might require finding all numbers of the Fibonacci sequence up to this position.

Terms in a Fibonacci sequence

The nth term of the Fibonacci sequence is the sum of term (n βˆ’ 1) and term (n βˆ’ 2) - provided n is greater than 2. Otherwise we know the first 2 terms are just 1.

nth term of Fibonacci sequences

1

Find the next term of the Fibonacci-type sequence: 1, 3, 4, 7, 11, ....

Find the next term of the Fibonacci-type sequence: 1, 3, 4, 7, 11, ....

2

Is 1, 1, 2, 3, 6 a part of the Fibonacci sequence?

Is 1, 1, 2, 3, 6 a part of the Fibonacci sequence?

3

Give the Fibonacci sequence up to the term 34.

Give the Fibonacci sequence up to the term 34.

4

Is 3, 4, 7, 11, 18, … a Fibonacci-type sequence?

Is 3, 4, 7, 11, 18, … a Fibonacci-type sequence?

5

Look at the Fibonacci Spiral given. What are the lengths of squares A and B?

Look at the Fibonacci Spiral given. What are the lengths of squares A and B?

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