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Questions and Answers
Which statement about the Fibonacci sequence is FALSE?
Which statement about the Fibonacci sequence is FALSE?
- Binet's Formula is the closed-form expression that allows direct calculation of Fibonacci numbers.
- Every number in the Fibonacci sequence is a prime number. (correct)
- The Fibonacci sequence starts with the numbers 0 and 1.
- The Golden Ratio Ï• is equal to $ rac{1+ ext{sqrt}{5}}{2}$.
What is the Golden Ratio Ï•?
What is the Golden Ratio Ï•?
- $ rac{1 + ext{sqrt}{10}}{2}$
- $ rac{ ext{sqrt}{5} - 1}{2}$
- $ rac{2 + ext{sqrt}{5}}{1}$
- $ rac{1 + ext{sqrt}{5}}{2}$ (correct)
What does Binet's Formula calculate?
What does Binet's Formula calculate?
- The sum of the first n Fibonacci numbers.
- The closed-form expression for Fibonacci numbers. (correct)
- The ratio of consecutive Fibonacci numbers.
- The limit of the Fibonacci sequence as n approaches infinity.
As n increases, what does the ratio F(n) / F(n-2) approach?
As n increases, what does the ratio F(n) / F(n-2) approach?
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Which statement about the starting numbers of the Fibonacci sequence is TRUE?
Which statement about the starting numbers of the Fibonacci sequence is TRUE?
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Study Notes
Fibonacci Sequence
- The Fibonacci sequence starts with 0 and 1, with each subsequent number being the sum of the two preceding ones. (Example: 0, 1, 1, 2, 3, 5, 8, 13, 21...)
- Not every number in the Fibonacci sequence is a prime number. Prime numbers are only divisible by 1 and themselves, while some Fibonacci numbers have more than two factors.
- The Golden Ratio (Ï•) is also known as the "divine proportion" and is approximately equal to 1.618.
- Binet's Formula is a closed-form expression that allows the direct calculation of any Fibonacci number without having to calculate all the preceding ones.
- The ratio between consecutive Fibonacci numbers (F(n) / F(n-1)) approaches the Golden Ratio as n increases. This relationship is a key property of the Fibonacci sequence.
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