Fibonacci Sequence Worksheet
Explore the Fibonacci sequence, its properties, and its appearance in nature and mathematics with this Grade 9 worksheet.
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Fibonacci Sequence Exploration
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Read each question carefully and provide your answers in the space provided. 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 six terms of the Fibonacci sequence are 0, 1, 1, 2, 3, and .
3. The mathematical formula for the Fibonacci sequence is F(n) = F(n-1) + F(n-2), where F(0) = 0 and F(1) = .
4. Calculate the 10th term of the Fibonacci sequence.
5. If F(n-1) = 34 and F(n) = 55, what is F(n+1)?
6. Which of the following is a property of the Fibonacci sequence?
Every term is an even number.
The ratio of consecutive terms approaches the Golden Ratio.
Each term is double the previous term.
The sequence only contains prime numbers.
7. The arrangement of seeds in a sunflower often follows a Fibonacci spiral pattern.
True
False
8. The number of petals on many flowers is often a Fibonacci number.
True
False
9. A pair of rabbits is placed on an island. A pair of rabbits does not breed until they are two months old. After two months, each pair produces another pair every month. If no rabbits die, how many pairs of rabbits will there be after 5 months?