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.

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 βˆ’ 1) and term (n βˆ’ 2) - provided n is greater than 2. Otherwise we know the first 2 terms are just 1.

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