20 Fibonacci numbers

20 Fibonacci numbers Image to Crop

How many Fibonacci Numbers?

Generate 20 Fibonacci numbers

We can do this two ways:

1) Recursive Algorithm

2) Binet's Formula

Recursive Algorithm:

F_n = F_{n - 1} + F_{n - 2}

where F₀ = 0 and F₁ = 1

Show Fibonacci Formula:

N/A + 0

N/A + 1

1 + 0 + 1

1 + 1 + 2

2 + 1 + 3

3 + 2 + 5

5 + 3 + 8

8 + 5 + 13

13 + 8 + 21

21 + 13 + 34

34 + 21 + 55

55 + 34 + 89

89 + 55 + 144

144 + 89 + 233

233 + 144 + 377

377 + 233 + 610

610 + 377 + 987

987 + 610 + 1,597

1,597 + 987 + 2,584

2,584 + 1,597 + 4,181

Use Binet's Formula

F_n = 1/√5(((1 + √5)/2)ⁿ - ((1 - √5)/2)ⁿ)

Given n = 19, we have:

F₁₉ = 0.44721359549996 * ((3.2360679774998/2)¹⁹ - (-1.2360679774998/2)¹⁹)

F₁₉ = 0.44721359549996 * ((1.6180339887499)¹⁹ - (-0.61803398874989)¹⁹)

F₁₉ = 0.44721359549996 * (9349.0001069633 - -0.00010696331036034)

F₁₉ = 0.44721359549996 * 9349.0002139266

F₁₉ = 4181

You have 1 free calculations remaining

F₁₉ = 4181

What is the Answer?

F₁₉ = 4181

How does the Fibonacci Sequence Calculator work?

Free Fibonacci Sequence Calculator - Generates a list of the first 100 Fibonacci numbers. Also shows how to generate the nth Fibonacci number using Binet‘s Formula
This calculator has 1 input.

What 1 formula is used for the Fibonacci Sequence Calculator?

F_n = F_{n - 1} + _{n - 2} where F₀ = 0 and F₁ = 1

For more math formulas, check out our Formula Dossier

What 8 concepts are covered in the Fibonacci Sequence Calculator?

algorithm: A process to solve a problem in a set amount of time
fibonacci: a number, commonly denoted F_n, which form the Fibonacci sequence, in which each number is the sum of the two preceding ones
fibonacci sequence
formula: a fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.
generator: software algorithm that generates a number that is taken from a limited or unlimited distribution and outputs it
number: an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
recursive algorithm: an algorithm which calls itself with smaller (or simpler) input values, and which obtains the result for the current input by applying simple operations to the returned value for the smaller (or simpler) input.
sequence: an arrangement of numbers or collection or objects in a particular order