- Write a program in Java to print Fibonacci series without recursion.
- How to generate Fibonacci series using recursion.

**Fibonacci series** is a series of integers, where N^{th} term is equal to the sum of N-1^{th} and N-2^{th}(last two terms). The first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent term is the sum of the previous two terms.

**0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ....**

## Java program to generate fibonacci series

**Algorithm to generate fibonacci series**

- First two terms of fibonacci series is 0 and 1.
- we will store the last two terms of fibonacci series in "last" and "secondLast" integer variable.
- Current term of fibonacci series is equal to the sum of "last" and "secondLast" term.(current = last + secondLast)
- Update last and secondLast variable as secondLast = last; and last = current;

package com.tcc.java.programs; import java.util.*; public class FibonacciSeries { public static void main(String args[]) { int terms, last = 1, secondLast = 0, current, i; Scanner in = new Scanner(System.in); System.out.println("Enter number of terms in Fibonacci Series"); terms = in.nextInt(); /* * Nth term = (N-1)th thrm + (N-2)th term; */ for(i = 0; i < terms; i++){ if(i < 2){ current = i; } else { current = last + secondLast; secondLast = last; last = current; } System.out.print(current + " "); } } }Output

Enter number of terms in Fibonacci Series 10 0 1 1 2 3 5 8 13 21 34

## Java program to print fibonacci series using recursion

In mathematical terms, the Nth term of Fibonacci series is defined by the recurrence relation:

- fibonacci(N) = Nth term in fibonacci series
- fibonacci(N) = fibonacci(N - 1) + fibonacci(N - 2);
- whereas, fibonacci(0) = 0 and fibonacci(1) = 1

In this program, we will write a user defined recursive function "int fibonacci(int N)" which returns N^{th} fibonacci number.

package com.tcc.java.programs; import java.util.*; public class FibonacciSeriesRecursion { public static void main(String args[]) { int terms, i; Scanner in = new Scanner(System.in); System.out.println("Enter number of terms in Fibonacci Series"); terms = in.nextInt(); /* * fibonacci(N) = fibonacci(N-1) + fibonacci(N-2); */ for(i = 0; i < terms; i++){ System.out.print(fibonacci(i) + " "); } } public static int fibonacci(int num){ /* Exit condition of recursion*/ if(num < 2) return num; return fibonacci(num - 1) + fibonacci(num - 2); } }Output

Enter number of terms in Fibonacci Series 12 0 1 1 2 3 5 8 13 21 34 55 89