Fibonacci Sequence

The Fibonacci sequence is a series of numbers in which each number (after the first two) is the sum of the two preceding ones. The sequence starts with 0 and 1, and the subsequent numbers are obtained by adding the last two numbers in the sequence. The sequence is named after the Italian mathematician Leonardo of Pisa, known as Fibonacci.

Formula

The Fibonacci sequence can be defined by the following recursive formula:

Where:

• Fn is the nth term in the sequence
• Fn-1 is the (n-1)th term
• Fn-2 is the (n-2)th term

Sequence

The Fibonacci sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on.

Study Guide

To understand the Fibonacci sequence, follow these steps:

1. Start with 0 and 1: The sequence always starts with 0 and 1.
2. Add the previous two numbers: To generate the next number in the sequence, add the last two numbers together.
3. Repeat: Continue this process to generate the entire sequence of Fibonacci numbers.

Applications

The Fibonacci sequence appears in many natural and man-made phenomena, including patterns in plants, the arrangement of leaves on a stem, and the spiral shapes of shells and galaxies. The sequence also has applications in computer algorithms, financial modeling, and art and design.

Understanding the Fibonacci sequence can provide a basis for exploring various mathematical concepts and real-world applications.