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Questions and Answers
The Fibonacci sequence starts with the numbers 0 and 1.
The Fibonacci sequence starts with the numbers 0 and 1.
True (A)
Every number in the Fibonacci sequence is a prime number.
Every number in the Fibonacci sequence is a prime number.
False (B)
The Golden Ratio ϕ is equal to $ rac{1+ ext{√}5}{2}$.
The Golden Ratio ϕ is equal to $ rac{1+ ext{√}5}{2}$.
True (A)
Binet's Formula is the closed-form expression that allows direct calculation of Fibonacci numbers.
Binet's Formula is the closed-form expression that allows direct calculation of Fibonacci numbers.
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The ratio F(n) / F(n-2) in the Fibonacci sequence approaches the Golden Ratio as n increases.
The ratio F(n) / F(n-2) in the Fibonacci sequence approaches the Golden Ratio as n increases.
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Study Notes
Fibonacci Sequence Properties
- The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones.
- Not every number in the Fibonacci sequence is a prime number. Many Fibonacci numbers are composite, meaning they have factors other than 1 and themselves.
- The Golden Ratio ϕ is equal to (1+√5)/2, an irrational number approximately equal to 1.618.
- Binet's Formula is a closed-form expression that allows direct calculation of any Fibonacci number without having to calculate all the preceding numbers.
- The ratio F(n) / F(n-2) in the Fibonacci sequence approaches the Golden Ratio as n increases. This is an important property that connects the sequence to this fundamental mathematical constant.
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