Calculators & Tools

Fibonacci Numbers & Sequence

Fibonacci sequence is a sequence of numbers, where each number is the sum of the 2 previous numbers, except the first two numbers that are 0 and 1.

• Fibonacci sequence formula
• Golden ratio convergence
• Fibonacci sequence table
• Fibonacci sequence calculator
• C++ code of Fibonacci function

Fibonacci sequence formula

For example:

F₀ = 0

F₁ = 1

F₂ = F₁+F₀ = 1+0  = 1

F₃ = F₂+F₁ = 1+1  = 2

F₄ = F₃+F₂ = 2+1  = 3

F₅ = F₄+F₃ = 3+2  = 5

...

Golden ratio convergence

The ratio of two sequential Fibonacci numbers, converges to the golden ratio:

φ is the golden ratio = (1+√5) / 2 ≈ 1.61803399

Fibonacci sequence table

n	Fn
0	0
1	1
2	1
3	2
4	3
5	5
6	8
7	13
8	21
9	34
10	55
11	89
12	144
13	233
14	377
15	610
16	987
17	1597
18	2584
19	4181
20	6765

Fibonacci sequence calculator

TBD

C code of Fibonacci function

double Fibonacci(unsigned int n)

{

    double f_n =n;

    double f_n1=0.0;

    double f_n2=1.0;

 

    if( n > 1 ) {

        for(int k=2; k<=n; k++) {

            f_n  = f_n1 + f_n2;

            f_n2 = f_n1;

            f_n1 = f_n;

        }

    }

 

    return f_n;

}