A triangular array of numbers where each entry is the sum of the two entries above it.

A triangular array of numbers where each entry is the product of the two entries above it.

A triangular array of numbers where each entry is the difference of the two entries above it.

A triangular array of numbers where each entry is the quotient of the two entries above it.

$$f(x) = \sum_{n=0}^\infty a_n x^n$$

$$f(x) = \prod_{n=0}^\infty a_n x^n$$

$$f(x) = \sum_{n=0}^\infty a_n x^{-n}$$

$$f(x) = \prod_{n=0}^\infty a_n x^{-n}$$

$$a_n = a_{n-1} + a_{n-2}$$

$$a_n = a_{n-1} * a_{n-2}$$

$$a_n = a_{n-1} - a_{n-2}$$

$$a_n = a_{n-1} / a_{n-2}$$

The Fibonacci sequence

The Pascal triangle

The Catalan numbers

The Stirling numbers of the second kind

Counting

Probability

Number theory

All of the above

$$f(x) = \frac{x}{1-x-x^2}$$

$$f(x) = \frac{x}{1-x+x^2}$$

$$f(x) = \frac{x}{1+x-x^2}$$

$$f(x) = \frac{x}{1+x+x^2}$$

$$a_n = a_{n-1} + a_{n-2}$$

$$a_n = a_{n-1} * a_{n-2}$$

$$a_n = a_{n-1} - a_{n-2}$$

$$a_n = a_{n-1} / a_{n-2}$$

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...

$$F_n = \frac{\phi^n - \psi^n}{\sqrt{5}}$$

$$F_n = \frac{\phi^n + \psi^n}{\sqrt{5}}$$

$$F_n = \frac{\phi^n - \psi^n}{\sqrt{5}} + 1$$

$$F_n = \frac{\phi^n + \psi^n}{\sqrt{5}} + 1$$

$$\phi = \frac{1 + \sqrt{5}}{2}$$

$$\phi = \frac{1 - \sqrt{5}}{2}$$

$$\phi = \frac{\sqrt{5} + 1}{2}$$

$$\phi = \frac{\sqrt{5} - 1}{2}$$

The limit of the ratio of consecutive Fibonacci numbers is the golden ratio.

The golden ratio is the average of two consecutive Fibonacci numbers.

The golden ratio is the square root of the sum of two consecutive Fibonacci numbers.

The golden ratio is the product of two consecutive Fibonacci numbers.

Art and design

Architecture

Nature

All of the above

A triangular array of numbers where each entry is the sum of the two entries above it.

A triangular array of numbers where each entry is the product of the two entries above it.

A triangular array of numbers where each entry is the difference of the two entries above it.

A triangular array of numbers where each entry is the quotient of the two entries above it.

$$f(x) = \frac{1}{1-x-x^2}$$

$$f(x) = \frac{1}{1-x+x^2}$$

$$f(x) = \frac{1}{1+x-x^2}$$

$$f(x) = \frac{1}{1+x+x^2}$$

$$a_n = a_{n-1} + a_{n-2}$$

$$a_n = a_{n-1} * a_{n-2}$$

$$a_n = a_{n-1} - a_{n-2}$$

$$a_n = a_{n-1} / a_{n-2}$$