Fibonacci Numbers Worksheet
Explore the fascinating world of Fibonacci numbers, their sequence, and their presence in nature.
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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?
The spiral arrangement of sunflower seeds
The branching patterns of trees
The shape of snowflakes
The growth of crystals
The ratio of consecutive Fibonacci numbers approaches the Golden Ratio (approximately 1.618).
All even numbers are part of the Fibonacci sequence.
Explain in your own words why the Fibonacci sequence is often found in nature. Provide at least two examples.
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