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Fibonacci Sequence Exploration

Explore the fascinating Fibonacci sequence with this worksheet, covering its definition, calculation, and presence in nature.

Grade 10 Math Sequences and SeriesFibonacci Sequence
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Includes

Short AnswerFill in the BlanksMultiple ChoiceTrue / FalseMatchingLong Answer

Standards

CCSS.MATH.CONTENT.HSF.BF.A.1.A

Topics

FibonacciSequenceMathematicsGrade 10
8 sections · Free to use · Printable
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Fibonacci Sequence Exploration

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Read each question carefully and provide your answers in the spaces provided. Show all your work for full credit.

1. What is the definition of the Fibonacci sequence? Describe how each number in the sequence is generated.

2. Complete the first ten terms of the Fibonacci sequence, starting with F₀ = 0 and F₁ = 1:

0, 1, 1, 2, 3, 5,  ,  ,  ,  

3. Which of the following is NOT a property often associated with the Fibonacci sequence?

a

Each number is the sum of the two preceding ones.

b

The ratio of consecutive numbers approaches the golden ratio.

c

It is an arithmetic sequence.

d

It appears frequently in nature.

4. True or False: The number of petals on many flowers often follows a Fibonacci number.

T

True

F

False

5. Match the Fibonacci sequence term to its correct value.

F₅

 

a. 8

F₈

 

b. 5

F₆

 

c. 13

6. Research and describe one real-world example (other than flower petals) where the Fibonacci sequence or the golden ratio can be observed. Explain how it relates to the sequence.