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Fibonacci Numbers Worksheet

Explore the fascinating world of Fibonacci numbers, their sequence, and their presence in nature.

Grade 9 Math Sequences and SeriesFibonacci Numbers
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Fill in the Blanks2 Short AnswerMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.SSE.B.4CCSS.MATH.CONTENT.HSF.BF.A.1a

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Fibonaccisequencemathgrade 9
7 sections · Free to use · Printable
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Fibonacci Numbers: The Nature's Code

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Read each question carefully and provide your best answer. Show all your work for full credit.

The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones. The first few terms are 0, 1, 1, 2, 3, 5, 8, 13,  ,  ,  . The 10th Fibonacci number is  .

In the Fibonacci sequence, F(n) = F(n-1) + F(n-2). If F(7) = 13 and F(8) = 21, then F(9) would be  . This property is known as a   relation.

1. What is the 12th Fibonacci number?

2. If the 6th Fibonacci number is 8 and the 7th is 13, what is the 5th Fibonacci number?

Which of the following natural phenomena often exhibits Fibonacci numbers or the Golden Ratio?

A

The spiral arrangement of sunflower seeds

B

The branching patterns of trees

C

The shape of snowflakes

D

The growth of crystals

The ratio of consecutive Fibonacci numbers approaches the Golden Ratio (approximately 1.618).

True
False

All even numbers are part of the Fibonacci sequence.

True
False

Explain in your own words why the Fibonacci sequence is often found in nature. Provide at least two examples.