100 Fibonacci numbers -

How many Fibonacci Numbers?

Generate 100 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

7,778,742,049 + 4,807,526,976 + 12,586,269,025

12,586,269,025 + 7,778,742,049 + 20,365,011,074

20,365,011,074 + 12,586,269,025 + 32,951,280,099

32,951,280,099 + 20,365,011,074 + 53,316,291,173

53,316,291,173 + 32,951,280,099 + 86,267,571,272

86,267,571,272 + 53,316,291,173 + 139,583,862,445

139,583,862,445 + 86,267,571,272 + 225,851,433,717

225,851,433,717 + 139,583,862,445 + 365,435,296,162

365,435,296,162 + 225,851,433,717 + 591,286,729,879

591,286,729,879 + 365,435,296,162 + 956,722,026,041

956,722,026,041 + 591,286,729,879 + 1,548,008,755,920

1,548,008,755,920 + 956,722,026,041 + 2,504,730,781,961

2,504,730,781,961 + 1,548,008,755,920 + 4,052,739,537,881

4,052,739,537,881 + 2,504,730,781,961 + 6,557,470,319,842

6,557,470,319,842 + 4,052,739,537,881 + 10,610,209,857,723

10,610,209,857,723 + 6,557,470,319,842 + 17,167,680,177,565

17,167,680,177,565 + 10,610,209,857,723 + 27,777,890,035,288

27,777,890,035,288 + 17,167,680,177,565 + 44,945,570,212,853

44,945,570,212,853 + 27,777,890,035,288 + 72,723,460,248,141

72,723,460,248,141 + 44,945,570,212,853 + 117,669,030,460,994

117,669,030,460,994 + 72,723,460,248,141 + 190,392,490,709,135

190,392,490,709,135 + 117,669,030,460,994 + 308,061,521,170,129

308,061,521,170,129 + 190,392,490,709,135 + 498,454,011,879,264

498,454,011,879,264 + 308,061,521,170,129 + 806,515,533,049,393

806,515,533,049,393 + 498,454,011,879,264 + 1,304,969,544,928,657

1,304,969,544,928,657 + 806,515,533,049,393 + 2,111,485,077,978,050

2,111,485,077,978,050 + 1,304,969,544,928,657 + 3,416,454,622,906,707

3,416,454,622,906,707 + 2,111,485,077,978,050 + 5,527,939,700,884,757

5,527,939,700,884,757 + 3,416,454,622,906,707 + 8,944,394,323,791,464

8,944,394,323,791,464 + 5,527,939,700,884,757 + 14,472,334,024,676,220

14,472,334,024,676,220 + 8,944,394,323,791,464 + 23,416,728,348,467,684

23,416,728,348,467,684 + 14,472,334,024,676,220 + 37,889,062,373,143,904

37,889,062,373,143,904 + 23,416,728,348,467,684 + 61,305,790,721,611,592

61,305,790,721,611,592 + 37,889,062,373,143,904 + 99,194,853,094,755,504

99,194,853,094,755,504 + 61,305,790,721,611,592 + 160,500,643,816,367,104

160,500,643,816,367,104 + 99,194,853,094,755,504 + 259,695,496,911,122,592

259,695,496,911,122,592 + 160,500,643,816,367,104 + 420,196,140,727,489,664

420,196,140,727,489,664 + 259,695,496,911,122,592 + 679,891,637,638,612,224

679,891,637,638,612,224 + 420,196,140,727,489,664 + 1,100,087,778,366,101,888

1,100,087,778,366,101,888 + 679,891,637,638,612,224 + 1,779,979,416,004,714,240

1,779,979,416,004,714,240 + 1,100,087,778,366,101,888 + 2,880,067,194,370,816,000

2,880,067,194,370,816,000 + 1,779,979,416,004,714,240 + 4,660,046,610,375,530,496

4,660,046,610,375,530,496 + 2,880,067,194,370,816,000 + 7,540,113,804,746,346,496

7,540,113,804,746,346,496 + 4,660,046,610,375,530,496 + 12,200,160,415,121,876,992

12,200,160,415,121,876,992 + 7,540,113,804,746,346,496 + 19,740,274,219,868,225,536

19,740,274,219,868,225,536 + 12,200,160,415,121,876,992 + 31,940,434,634,990,100,480

31,940,434,634,990,100,480 + 19,740,274,219,868,225,536 + 51,680,708,854,858,326,016

51,680,708,854,858,326,016 + 31,940,434,634,990,100,480 + 83,621,143,489,848,426,496

83,621,143,489,848,426,496 + 51,680,708,854,858,326,016 + 135,301,852,344,706,760,704

135,301,852,344,706,760,704 + 83,621,143,489,848,426,496 + 218,922,995,834,555,203,584

Use Binet's Formula

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

Given n = 99, we have:

F99 = 0.44721359549996 * ((3.2360679774998/2)99 - (-1.2360679774998/2)99)

F99 = 0.44721359549996 * ((1.6180339887499)99 - (-0.61803398874989)99)

F99 = 0.44721359549996 * (4.8952670052397E+20 - -2.0427894922374E-21)

F99 = 0.44721359549996 * 4.8952670052397E+20

F99 = 2.1892299583456E+20

What is the Answer?

F99 = 2.1892299583456E+20

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?

Fn = Fn - 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?

algorithmA process to solve a problem in a set amount of timefibonaccia number, commonly denoted Fn, which form the Fibonacci sequence, in which each number is the sum of the two preceding onesfibonacci sequenceformulaa fact or a rule written with mathematical symbols. A concise way of expressing information symbolically.generatorsoftware algorithm that generates a number that is taken from a limited or unlimited distribution and outputs itnumberan 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 algorithman 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.sequencean arrangement of numbers or collection or objects in a particular order

Example calculations for the Fibonacci Sequence Calculator

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