Fibonacci Numbers Worksheet
Explore the fascinating world of Fibonacci numbers, their patterns, and their relationship with the Golden Ratio.
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Fibonacci Numbers Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. The Fibonacci sequence starts with 0 and 1, and each subsequent number is the of the two preceding ones.
2. The first 10 terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, , 34.
3. The ratio of consecutive Fibonacci numbers approaches a special number known as the .
1. Find the 12th term in the Fibonacci sequence. Show your work.
2. If F(n) represents the nth Fibonacci number, and F(n-1) = 55 and F(n) = 89, what is F(n+1)?
1. Which of the following is NOT a property of Fibonacci numbers?
Every third Fibonacci number is even.
The sum of the first n Fibonacci numbers is F(n+2) - 1.
The ratio of two consecutive Fibonacci numbers is always an integer.
Fibonacci numbers appear in nature, such as in plant growth patterns.
1. The Golden Ratio is approximately 1.618.
True
False
2. The ratio of F(n+1) / F(n) gets closer to the Golden Ratio as n increases.
True
False
1. Describe one real-world example where Fibonacci numbers or the Golden Ratio can be observed.