Fibonacci Sequence Calculator

How to Calculate Fibonacci Numbers

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It starts with 0 and 1, and each subsequent number is found by adding the two numbers before it.

Formula

The formula for the Fibonacci sequence is:

\[ F(n) = F(n-1) + F(n-2) \]

Where:

• F(n) is the nth Fibonacci number
• F(n-1) is the (n-1)th Fibonacci number
• F(n-2) is the (n-2)th Fibonacci number

With initial conditions:

\[ F(0) = 0, F(1) = 1 \]

Calculation Steps

1. Start with F(0) = 0 and F(1) = 1.
2. For each subsequent number, add the two preceding numbers.
3. Continue this process until you reach the desired nth term.

Example

Let's calculate the first 8 Fibonacci numbers:

1. F(0) = 0
2. F(1) = 1
3. F(2) = F(1) + F(0) = 1 + 0 = 1
4. F(3) = F(2) + F(1) = 1 + 1 = 2
5. F(4) = F(3) + F(2) = 2 + 1 = 3
6. F(5) = F(4) + F(3) = 3 + 2 = 5
7. F(6) = F(5) + F(4) = 5 + 3 = 8
8. F(7) = F(6) + F(5) = 8 + 5 = 13

Visual Representation

This diagram illustrates the first 8 Fibonacci numbers, showing how each number is the sum of the two preceding ones.