Generate 50 Fibonacci numbers
We can do this two ways:
1) Recursive Algorithm
2) Binet's Formula
Recursive Algorithm:
Fn = Fn - 1 + Fn - 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
4,181 + 2,584 + 6,765
6,765 + 4,181 + 10,946
10,946 + 6,765 + 17,711
17,711 + 10,946 + 28,657
28,657 + 17,711 + 46,368
46,368 + 28,657 + 75,025
75,025 + 46,368 + 121,393
121,393 + 75,025 + 196,418
196,418 + 121,393 + 317,811
317,811 + 196,418 + 514,229
514,229 + 317,811 + 832,040
832,040 + 514,229 + 1,346,269
1,346,269 + 832,040 + 2,178,309
2,178,309 + 1,346,269 + 3,524,578
3,524,578 + 2,178,309 + 5,702,887
5,702,887 + 3,524,578 + 9,227,465
9,227,465 + 5,702,887 + 14,930,352
14,930,352 + 9,227,465 + 24,157,817
24,157,817 + 14,930,352 + 39,088,169
39,088,169 + 24,157,817 + 63,245,986
63,245,986 + 39,088,169 + 102,334,155
102,334,155 + 63,245,986 + 165,580,141
165,580,141 + 102,334,155 + 267,914,296
267,914,296 + 165,580,141 + 433,494,437
433,494,437 + 267,914,296 + 701,408,733
701,408,733 + 433,494,437 + 1,134,903,170
1,134,903,170 + 701,408,733 + 1,836,311,903
1,836,311,903 + 1,134,903,170 + 2,971,215,073
2,971,215,073 + 1,836,311,903 + 4,807,526,976
4,807,526,976 + 2,971,215,073 + 7,778,742,049
Use Binet's Formula
Fn = 1/√5(((1 + √5)/2)n - ((1 - √5)/2)n)
Given n = 49, we have:
F49 = 0.44721359549996 * ((3.2360679774998/2)49 - (-1.2360679774998/2)49)
F49 = 0.44721359549996 * ((1.6180339887499)49 - (-0.61803398874989)49)
F49 = 0.44721359549996 * (17393796001 - -5.7491763151788E-11)
F49 = 0.44721359549996 * 17393796001
Final Answer
What is the Answer?
How does the Fibonacci Sequence Calculator work?
This calculator has 1 input.
What 1 formula is used for the Fibonacci Sequence Calculator?
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 Fn, 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
