Fibonacci Sequence Exploration

Fibonacci Sequence Exploration

Read each question carefully and provide your best answer. Show all your work where applicable.

1. The Fibonacci sequence starts with 0 and 1, and each subsequent number is the   of the two preceding ones.

2. The first 7 numbers in the Fibonacci sequence are 0, 1, 1, 2, 3, 5, and  .

3. Which of the following numbers is NOT a Fibonacci number?

4. What is the 10th number in the Fibonacci sequence (starting with F0 = 0, F1 = 1)?

5. A Fibonacci spiral is created by drawing quarter circles in a series of connected squares with side lengths equal to Fibonacci numbers. Draw the next two squares and the corresponding quarter circles to extend the spiral shown below. Label the side lengths of your new squares.

6. The number of petals on many flowers often follows a Fibonacci number.

7. As the Fibonacci sequence progresses, the ratio of consecutive Fibonacci numbers (F(n) / F(n-1)) approaches a special irrational number. What is this number called?