Fibonacci Sequence Exploration

Explore the fascinating world of the Fibonacci sequence, its properties, and its appearance in nature.

Grade 8 Math Sequences and SeriesFibonacci Sequence

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Fill in the BlanksMultiple Choice2 Short AnswerCustomTrue / False

Standards

CCSS.MATH.CONTENT.8.F.A.3CCSS.MATH.CONTENT.HSA.SSE.A.1

8 sections · Free to use · Printable

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Fibonacci Sequence Exploration

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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.

True

False

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?