Fibonacci sequence

The Fibonacci sequence has many uses. In this sequence, each number is the sum of the previous two numbers.

In the 1200s Fibonacci published the sequence, showing its use in collecting interest. The sequence has been shown to have many other uses.

Example

This is an iterative implementation of the Fibonacci sequence, where we compute numbers in a loop. We use a temporary variable to copy the previous number.

Module Module1

    Function Fibonacci(ByVal n As Integer) As Integer
        Dim a As Integer = 0
        Dim b As Integer = 1

        ' Add up numbers.
        For i As Integer = 0 To n - 1
            Dim temp As Integer = a
            a = b
            b = temp + b
        Next

        Return a
    End Function

    Sub Main()
        ' Display first 10 Fibonacci numbers.
        For i As Integer = 0 To 10
            Console.WriteLine(Fibonacci(i))
        Next
    End Sub

End Module
0
1
1
2
3
5
8
13
21
34
55

Function notes

We use a Function, not a Sub, because a return value is required. If we cached the values in a list (a lookup table) this would be faster.

A recursive method can be used to compute Fibonacci numbers: each value is defined as the sum of the previous two. But an iterative solution is often easier to read and understand.