# Java Program to Display Fibonacci Series

## What is a Fibonacci Series ?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, beginning with 0 and ending with 1. The number sequence is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

## Steps to Find the Factorial of a Number :

1. Create two variables, “a” and “b”, and set their values to 0 and 1.
2. Then, add “a” and “b” and store the sum in “b”.
3. And update “a” with the previously calculated value of “b”.
4. Repeat this process n times and store each new value of “b” in a list to obtain the Fibonacci series.

### Code example for the above algorithm :

```public static void fibonacci(int n) {
int a = 0, b = 1;
System.out.print(a + " " + b);

for (int i = 2; i < n; i++) {
int c = a + b;
System.out.print(" " + c);
a = b;
b = c;
}
}
```

### Code example for recursion method :

```function fibonacci(n)
if n <= 1
return n
else
return fibonacci(n-1) + fibonacci(n-2)
```

### Example : Using a for loop

Run

```public class Main {
public static void main(String[] args) {
int n = 10;
int a = 0, b = 1;
System.out.print(a + " " + b);

for (int i = 2; i < n; i++) {
int c = a + b;
System.out.print(" " + c);
a = b;
b = c;
}
}
}

```

### Output :

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

#### Explanation :

This program generates the Fibonacci sequence up to n, where n in this example is set to 10. It begins by declaring and initializing the variables n, a, and b. It then prints the first two numbers in the sequence, 0 and 1. Following that, it employs a for loop to calculate and print the next n-2 numbers in the sequence. The program accomplishes this by adding the sequence’s two previous numbers, assigning the sum to the variable c, and then setting a to b and b to c. It then prints c and continues this process until the for loop is finished.

### Example : Using recursion

Run
```public class Main {
public static int fibonacci(int n) {
if (n <= 1) {
return n;
} else {
return fibonacci(n-1) + fibonacci(n-2);
}
}

public static void main(String[] args) {
int n = 10;
for (int i = 0; i < n; i++) {
System.out.print(fibonacci(i) + " ");
}
}
}

```

### Output :

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

#### Explanation :

In this example, The fibonacci() function is a recursive function that calculates the nth term of the Fibonacci series. It takes an integer n as an argument and returns an integer. If n is 0 or 1, it returns n as the result. If n is greater than 1, it returns the sum of the n-1th term and the n-2th term of the Fibonacci series. The calculation is done by calling the fibonacci() function recursively with n-1 and n-2 as arguments.

### Example : Using while loop

Run
```public class Main {
public static void main(String[] args) {
int n = 10;
int a = 0, b = 1;
int c;
System.out.print(a + " " + b);

int i = 2;
while (i < n) {
c = a + b;
System.out.print(" " + c);
a = b;
b = c;
i++;
}
}
}

```

### Output :

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

#### Explanation :

• In the above code, we first declare and initialize three integer variables a, b, and c. a and b have initial values of 0 and 1, respectively, and c has not yet been initialized. The initial values of a and b are then printed to the console.
• Following that, we declare and assign the integer variable i the value 2. I’s purpose is to keep track of how many terms we’ve printed so far.
• The while loop will continue to run as long as i is less than n. In each loop iteration, we calculate and store the next term of the Fibonacci series, which is the sum of a and b. After that, we print c to the console. Following that, we update the values of a and b to be b and c, respectively. Finally, we increment the value of i by 1.
• We have found and printed the first n terms of the Fibonacci series after the while loop has completed. The program’s output will be the same as in the previous example: 0 1 1 2 3 5 8 13 21 34.

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