### What is Fibonacci Series?

A Fibonacci series is a sequence of numbers where each number is the sum of the previous two numbers. The series starts from two numbers 0 and 1. They are in the fowling sequence:

This series generates next number in series by adding the previous two numbers. It starts the sequence of series using two numbers − F0 & F1. With the starting values of F0 & F1 to start the series 0, 1 or 1, 1 respectively.

**either **

0,1,1,2,3,5,8,13,21,34,55,.,.,.,.,.,.,. and so on

**or if it starts with 1 then**

1,1,2,3,5,8,11,19,30,49,79........ and so on.

## Fibonacci Series Examples

**In mathematical terminology, each number is in the form of:**

`Fn = Fn-1 + Fn-2`

**In this tutorial, we will Study**

- Fibonacci Series Algorithm
- Fibonacci Series using Recursion
- Fibonacci Series without Recursion
- Fibonacci Series using Function
- Fibonacci Series Java Program
- Fibonacci Series in C
- Fibonacci Series Python Example
- Fibonacci Series C++ Program

### Fibonacci Series Algorithm

Fibonacci sequence** **algorithm starts with 1 we can write it as

```
sq (1) = sq (0) = 1.
sq (n) = sq ( n-1 ) + sq ( n-2 ) for n >= 2
```

Fibonacci numbers starts with (starting sq (0)) 1, 1, 2, 3, 5, 8 ...

simply we can say the n-th Fibonacci number is the sum of the prior 2. As said in the explanation.

If you want to start with 0 then you have assigned 0 to sq (1)=sq(0)=0.

**To understand in the elaborated way of Algorithm**

**1) **Start

**2)** Variables Declaration L, A, B, display

**3) **Value assign to variables, A=0, B=1, and Display =0

**4) **Assign the series sequence to be run

**5) **Print starting two number terms of series using variable previously caring values 0,1 (in A, B respectively).

**6) **Start the loop using the loop variable

- -> Display =A+B
- -> A=B
- -> B=Display
- -> increase loop value of L by 1
- -> print the value of Display

**7) **End

### Fibonacci Series Methods

**There are 2 methods to Display Fibonacci Sequence:**

- Fibonacci Series using Recursion
- Fibonacci Series without Recursion

### Fibonacci Series using Recursion

```
#include<stdio.h>
#include<conio.h>
void main()
{
int fibonacci(int ) ;
int i,s,n;
clrscr();
printf("Number of elements in the list n");
scanf("%d",&n);
printf("Fibonacci series is :n");
for(i=1;i<=n;i++)
{
s= fibonacci(i);// Calling with Argument
printf("%5d",s);
}
getch();
}
// Function definition
int fibonacci(int x)
{
int f;
if (x==1)
return(0);
else if (x==2)
return(1);
else
f= fibonacci(x-1)+fibonacci(x-2);
return(f);
}
```

**Output**

Let the limit of element entered be 5

Hence, the output

**Fibonacci series is:**

0 1 1 2 3

### Fibonacci Series without Recursion

```
#include<stdio.h>
int main()
{
int n1=0,n2=1,n3,i,number;
printf("Number of elements in the list:");
scanf("%d",&number);
printf("n%d %d",n1,n2);
for(i=2;i<number;++i)
{
n3=n1+n2;
printf(" %d",n3);
n1=n2;
n2=n3;
}
return 0;
}
```

**Output**

Let the limit of element entered be 5

Hence, the output

**Fibonacci series is: 0 1 1 2 3**

### Fibonacci Series using Function

```
#include<stdio.h>
#include<conio.h>
void main()
{
int fibonacci(int,int),n,i;
clrscr();
printf("Number of elements in the list:");
scanf("%d",&n);
printf(" 0 1");
fibonacci(i,n);
getch();
}
int fibonacci(int m,int n)
{
int a=0,b=1;
int c;
for(m=1;m<=n-2;m++)
{
c=a+b;
a=b;
b=c;
printf("t%d",c);
}
}
```

**Output**

Let the limit of element entered be 4

Hence, the output

**Fibonacci series is:**

0 1 1 2

### Fibonacci Series Java Program Example

```
public class FibSeries{
public static void main(String args[]) {
int val1, val2, val3, loi, nxt;
nxt = 10;
val1 = val2 = 1;
System.out.print("Fibonacci Series ");
System.out.print(val1+" "+val2);
for(loi = 1; loi <= nxt-2; loi++) {
val3 = val1 + val2;
System.out.print(" ");
System.out.print(val3);
val1 = val2;
val2 = val3;
}
}
}
```

**Output will be**

**$javac FibSeries.java**

**$java -Xmx128M -Xms16M FibSeries**

Fibonacci Series 1 1 2 3 5 8 13 21 34 55

### Fibonacci Series in C

```
#include <stdio.h>
int main()
{
int i, nt, num1 = 0, num2 = 1, nTerm;
printf("Enter the number of terms: ");
scanf("%d", &nt);
printf("Fibonacci Series: ");
for (i = 1; i <= nt; ++i)
{
printf("%d, ", num1);
nTerm = num1 + num2;
num1 = num2;
num2 = nTerm;
}
return 0;
}
```

**Output will be **

Enter the number of terms: 12

Fibonacci Series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,

### Fibonacci Series Python Example

```
# To print Fibonacci series, after taking no of terms input from user
loopterms = int(input("Please enetr the Loop Terms"))
num1 = 0
num2 = 1
total = 2
if loopterms <= 0:
print("Plese enter a positive integer")
elif loopterms == 1:
print("Fibonacci sequence:")
print(num1)
else:
print("Fibonacci sequence:")
print(num1,",",num2,end=', ')
while total < loopterms:
nth = num1 + num2
print(nth,end=' , ')
num1 = num2
num2 = nth
total += 1
```

**Output will be **

How many terms? 10

**Fibonacci sequence: **

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

### Fibonacci Series C++ Program Example

```
#include <iostream>
using namespace std;
int main()
{
int num1 = 0,i=2, num2 = 1, nTerm = 0, nput;
cout << "Enter a positive number: ";
cin >> nput;
// displays the first two terms which is always 0 and 1
cout << "Fibonacci Series: " << num1 << ", " << num2 << ", ";
nTerm = num1 + num2;
while(i < nput)
{
++i;
cout << nTerm << ", ";
num1 = num2;
num2 = nTerm;
nTerm = num1 + num2;
}
return 0;
}
```

**Output will be **

Enter the number of terms: 12

Fibonacci Series: 01 1 2 3 5 8 13 21 34 55 89