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Fibonacci Sequence & Golden Ratio

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Questions and Answers

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 ϕ is equal to $rac{1+ ext{sqrt}{5}}{2}$.

What is the Golden Ratio ϕ?

$rac{1 + ext{sqrt}{10}}{2}$

$rac{ ext{sqrt}{5} - 1}{2}$

$rac{2 + ext{sqrt}{5}}{1}$

$rac{1 + ext{sqrt}{5}}{2}$ (correct)

What does Binet's Formula calculate?

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?

<p>The Golden Ratio.</p> Signup and view all the answers

Which statement about the starting numbers of the Fibonacci sequence is TRUE?

<p>The sequence starts with 0 and 1.</p> Signup and view all the answers

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 (ϕ) 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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Description

Explore the intriguing world of the Fibonacci sequence, starting with 0 and 1, and discover how each number is formed by the sum of the two preceding numbers. Delve into concepts like prime numbers, the Golden Ratio, and Binet's Formula. This quiz will test your understanding of these fundamental mathematical principles.