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# 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 : **

- Create two variables,
**“a”**and**“b”**, and**set their values to 0 and 1.** - Then,
**add “a” and “b”**and**store the sum in “b”.** - And
**update “a”**with the previously calculated value of**“b”.** **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 **

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**

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 **

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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