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.
\[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...\]
Start with the numbers 1 and 1 (or 0 and 1) as the first two terms (Base Case).
Add the previous two terms together to obtain the next term in the sequence.
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 \(a_{5} = 5\).