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Fibonacci Sequence

The Fibonacci sequence is a special type of sequence. It starts with 0 and 1, then every subsequent number is the sum of the two preceding ones. Each number in the sequence is called a Fibonacci number.

A characteristic of the Fibonacci sequence is that the numbers start at 0, unlike other sequences where the first term starts at 1.

Here is the first few Fibonacci numbers.


It is also possible to have Fibonacci type sequences. These are sequences that do not start with 0 and 1 but they follow the characteristics of the Fibonacci sequence. Here is an example,

Lastly on this topic, there is a feature of the Fibonacci sequence which is worth highlighting here, which is the ‘Golden Ratio‘ – also known as the Magic Number‘. This number allows you to find any number in the Fibonacci sequence (nth Fibonacci number) using a formula, similar to the nth term of a sequence.

Note that this is not required required for the GCSE exam.