The Fibonacci Sequence

Hi. Here is a short guide on the Fibonacci sequence of numbers.

A sequence is a list of ordered objects. In a lot of cases, sequences are lists of ordered numbers. One example of a sequence is the set of even numbers such as 2, 4, 6, 8, etc. The first term in the sequence is 2, the second term being 4 and so on.

The Fibonacci sequence starts with the first two terms being 1 and 1 (or 0 and 1 as an alternate version). The third term would be the sum of the previous two terms which would be 1 + 1 = 2. The next term would be 1 + 2 = 3. The term after the 3 would be 3 + 2 = 5. The pattern continues by adding the previous two terms together to get the next term.

The Fibonacci sequence of numbers is an infinite (never-ending) sequence of numbers. Here are the first 10 terms of the Fibonacci sequence.

    \[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...\]


The Fibonacci Number Sequence (Simplified)

1) Start with the numbers 1 and 1 (or 0 and 1) as the first two terms (Base Case).

2) Add the previous two terms together to obtain the next term in the sequence.


The Fibonacci Number Sequence (Mathematical Version)

Assume that a_{n} for n = {1, 2, 3, ...} is the n-th term in the Fibonacci sequence. For example we have a_{1} = 1 and a_{5} = 5.

1) Start with a_{1} = 1 and a_{2} = 1 (or a_{1} = 0 and a_{2} = 1) as the first two terms.

2) For j = {3, 4, ...}, the next term a_{j} can be obtained using the formula a_{j} = a_{j - 1} + a_{j - 2}.

 

Leave a Reply