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How to Solve a Fibonacci Sequence

Leonardo Fibonacci's famous sequence has fascinated academics the world over for centuries. Initially developed to explain the breeding pattern of rabbits, it quickly became apparent that Fibonacci's sequence was applicable to a wide array of disparate natural phenomena, including flower petal patterns, the family structure of the honeybee, seashell spirals and much more. Since this realization, Fibonacci's sequence has been a focal point of debate, research and controversy. Despite this, solving a Fibonacci sequence remains a relatively simple task.

Instructions

    • 1

      Generate Fibonacci's sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...

    • 2

      Understand that the pattern is such that each term can be generated by the sum of the two terms that precedes it. For instance, the fourth Fibonacci term, or F(4), is equal to 3, which is the sum of the second Fibonacci term (1) and the third Fibonacci term (2).

    • 3

      Create a formula that corresponds to the pattern you have observed. Since the sequence shows that any term will be equal to the sum of the previous two terms, it follows that the formula should be: F(n) = F(n-1) + F(n-2). This means that any Fibonacci term---represented by the variable n---will equal the sum of the Fibonacci term that directly precedes it, or F(n-1), and the Fibonacci term that precedes it by two terms, or F(n-2).

    • 4

      Plug in any Fibonacci terms to the formula F(n) = F(n-1) + F(n-2) to solve the Fibonacci sequence for any Fibonacci term n.

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