**Java Programs**

➤ Check Even Number

➤ Check Odd Number

➤ Java Even-Odd

➤ Greatest of 3 numbers

➤ Exponents in Java

➤ Java Leap Year Program

➤ Display Multiplication Table

➤ Reverse of a number

➤ Factors of a Number

➤ Java LCM of 2 Numbers

➤ Java HCF of 2 Numbers

➤ Quadratic Equation Program

➤ Square Root of Number

➤ Perfect Square Program

➤ Simple Calculator Program

➤ BMI Calculator Java

➤ Factorial of a Number

➤ Factorial Using Recursion

**#**Java Programs to Find Sum

**#**Java Conversion Programs

**#**Java Program on Series

**#**Java Pattern Programs

**#**Java Number Programs

**Java Array Programs**

**Java String Programs**

Previously we developed the Fibonacci series program in java using iteration (for loop, while loop). Now in this post, we will develop the Fibonacci series program using the recursion technique in the Java programming language.

In the Fibonacci series, the next element is the sum of the previous two elements. The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it.

Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so forth. As a rule, the expression is X_{n}= X_{n-1}+ X_{n-2}

It is named after an Italian mathematician, Leonardo Fibonacci, who lived in the early thirteenth century. Fibonacci numbers are a series in which each number is the sum of the previous two numbers.

By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.

The base case for finding factorial

fibonacci(0) = 0

fibonacci(1) = 1

General case for finding factorial

fibonacci(n) = fibonacci(n-1) + fibonacci(n-2)

```
Algorithm:- fibonacci(n)
if (n<=1)
then return n
else
return fibonacci(n-1) + fibonacci(n-2)
```

## Fibonacci Recursive Java Method

Fibonacci recursive method using if-else statement,

```
public static int fibonacci(int n) {
if(n<=1) return n; // base case
else // general case
return (fibonacci(n-1) + fibonacci(n-2) );
}
```

Fibonacci recursive method using ternary operator,

Using a ternary operator the logic of the Fibonacci recursive method can be written within a single line.

```
public static int fibonacci(int n) {
return (n<=1) ? n :
(fibonacci(n-1) + fibonacci(n-2) );
}
```

## Finding Nth Fibonacci term

```
import java.util.Scanner;
public class FibonacciSeries {
public static int fibonacci(int n) {
if(n<=1) return n; // base case
else // general case
return (fibonacci(n-1) + fibonacci(n-2) );
}
public static void main(String[] args) {
int n; // range value
// Read range value
Scanner scan = new Scanner(System.in);
System.out.print("Enter n value: ");
n = scan.nextInt();
// find nth fibonacci term
System.out.println(n+"th Fibonacci term "
+ " is = "+ fibonacci(n));
// close Scanner class object
scan.close();
}
}
```

The output for the different test-cases:-

Enter n value: 7

7th Fibonacci term is = 13

Enter n value: 10

10th Fibonacci term is = 55

## Fibonacci Series using Recursion in Java

```
import java.util.Scanner;
public class FibonacciSeries {
public static int fibonacci(int n) {
return (n<=1) ? n :
(fibonacci(n-1) + fibonacci(n-2) );
}
public static void main(String[] args) {
int term; // range value
// Read range value
Scanner scan = new Scanner(System.in);
System.out.print("Enter the term: ");
term = scan.nextInt();
// display fibonacci series
System.out.println("First "+term+" terms of "
+ "Fibonacci series are: ");
for(int i=1; i<term; i++)
System.out.print(fibonacci(i)+"\t");
// close Scanner class object
scan.close();
}
}
```

The output for the different test-cases:-

Enter the term: 7

First 7 terms of Fibonacci series are:`1 1 2 3 5 8`

Enter the term: 15

First 15 terms of Fibonacci series are:`1 1 2 3 5 8 13 21 34 55 89 144 233 377`

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