Fibonacci Numbers Worksheet

Fibonacci Numbers Exploration

Read each question carefully and answer to the best of your ability. Show all your work where applicable. Remember the Fibonacci sequence starts with 0, 1, 1, 2, 3, 5, ... where each number is the sum of the two preceding ones.

1. The first two numbers in the Fibonacci sequence are   and  .

2. To find any number in the Fibonacci sequence, you add the   numbers before it.

3. The 7th Fibonacci number is  .

1. Write out the first 10 Fibonacci numbers, starting with F₀ = 0 and F₁ = 1.

2. What is the 12th Fibonacci number?

1. Which of the following numbers is a Fibonacci number?

2. What is the approximate value of the Golden Ratio (Phi), which is related to Fibonacci numbers?

1. Fibonacci numbers appear in nature, such as in the branching of trees and arrangement of leaves on a stem.

2. The Fibonacci sequence was discovered by a Greek mathematician named Euclid.

1. Imagine a pair of rabbits (one male, one female) are born in January. In February, they are one month old and can mate. In March, the female gives birth to a new pair of rabbits. If this pattern continues, and no rabbits die, how many pairs of rabbits will there be by July?

The Fibonacci sequence is closely related to the Golden Spiral. This spiral is formed by drawing quarter circles in a series of squares whose side lengths are Fibonacci numbers (1, 1, 2, 3, 5, 8, etc.).

Describe what you observe about the relationship between the squares and the spiral in the diagram above.