Edexcel GCSE Maths Fibonacci sequences
This page covers the following topics:
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.
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.
The nth term of the Fibonacci sequence is the sum of term (n − 1) and term (n − 2) - provided n is greater than 2. Otherwise we know the first 2 terms are just 1.
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