Exploring the Fibonacci Phenomenon

What are the first five numbers in the Fibonacci sequence?

• [0, 1, 2, 3, 5]

• [1, 2, 3, 5, 8]

• [0, 1, 1, 2, 3]

• [1, 1, 2, 4, 6]

Calculate the 10th Fibonacci number.

• 21

• 55

• 13

• 34

What is the formula to find the nth Fibonacci number?

• F(n) = F(n-1) - F(n-2)

• F(n) = F(n-1) + F(n-2) with F(0) = 0, F(1) = 1 or F(n) = (phi^n - (1-phi)^n) / sqrt(5)

• F(n) = F(n-1) * F(n-2)

• F(n) = n^2

How does the Fibonacci sequence start?

• 0, 1

• 1, 3

• 0, 2

• 1, 2

Identify the Fibonacci number that comes after 21.

• 13

• 55

• 34

• 8

In what year was the Fibonacci sequence introduced to the Western world?

• 1150

• 1225

• 1301

• 1202

How can the Fibonacci sequence be applied in computer algorithms?

• The Fibonacci sequence is used for sorting algorithms.

• The Fibonacci sequence is applied in image processing techniques.

• The Fibonacci sequence is used in dynamic programming, Fibonacci heaps, and efficient search algorithms.

• The Fibonacci sequence is utilized in network routing protocols.

Graph the first 10 Fibonacci numbers on a coordinate plane.

• The first 10 Fibonacci numbers are: (0,0), (1,1), (2,1), (3,2), (4,3), (5,5), (6,8), (7,13), (8,21), (9,34).

• (0,1)

• (2,3)

• (1,0)

What is the relationship between the Fibonacci sequence and the golden ratio?

• The golden ratio is a term used only in geometry, not in sequences.

• The Fibonacci sequence is unrelated to the golden ratio.

• The Fibonacci sequence converges to the golden ratio as the ratio of consecutive terms.

• The Fibonacci sequence decreases towards the golden ratio.

Name a natural phenomenon that exhibits the Fibonacci sequence.

• Leaf color change

• Water cycle stages

• Phyllotaxis in plants

• Photosynthesis process