Table of Contents

**Fibonacci Series in Java:** The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding ones, beginning with 0 and 1. This article will demonstrate how to generate the Fibonacci sequence in Java up to a specific term, denoted as N, where N represents the specified number.

In the Fibonacci sequence, each subsequent number is the total of the two preceding numbers. For instance, the sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. The sequence begins with the numbers 0 and 1.

**Also Check: Computer | Cache Memory**

**There are two methods to develop a program for the Fibonacci sequence in Java:**

- Fibonacci Sequence without recursion
- Fibonacci Sequence with recursion

## Fibonacci Series in Java without using recursion

**Initialize variables:**Start by initializing the first two numbers of the series. Usually, the first two numbers are 0 and 1.**Use a loop:**Use a loop to calculate the next numbers in the series by adding the last two numbers.**Update variables:**Update the variables to hold the last two numbers for the next iteration.

Here’s a Java program to generate the Fibonacci series without using recursion:

```
public class Fibonacci {
public static void main(String[] args) {
int n = 10; // Number of terms to display
int first = 0, second = 1;
System.out.println("Fibonacci Series without recursion:");
for (int i = 1; i <= n; ++i) {
System.out.print(first + " ");
// Compute the next term
int next = first + second;
// Update variables
first = second;
second = next;
}
}
}
```

### Explanation

**Variables Initialization:**

int first = 0, second = 1;

first and second are initialized to the first two numbers of the Fibonacci series.

**Loop through the series:**

```
for (int i = 1; i <= n; ++i) {
System.out.print(first + " ");
int next = first + second;
first = second;
second = next;
}/code>
```

- The loop runs n times to generate n terms of the series.
- System.out.print(first + ” “); prints the current term.
- int next = first + second; calculates the next term in the series.
- first = second; and second = next; update first and second for the next iteration.

**Output:**

The program will output the first 10 terms of the Fibonacci series:

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

## Fibonacci Series using recursion in java

- Define the Base Cases: The first two numbers in the Fibonacci series are 0 and 1. These are our base cases.
- Define the Recursive Case: For any other number in the series, it is the sum of the two preceding numbers. So, fibonacci(n) = fibonacci(n-1) + fibonacci(n-2).

Here’s a simple Java program to calculate the Fibonacci series using recursion:

```
public class Fibonacci {
// Method to calculate Fibonacci number
public static int fibonacci(int n) {
// Base cases
if (n == 0) {
return 0;
}
if (n == 1) {
return 1;
}
// Recursive case
return fibonacci(n - 1) + fibonacci(n - 2);
}
public static void main(String[] args) {
int number = 10; // Let's find the first 10 Fibonacci numbers
System.out.println("Fibonacci series up to " + number + " terms:");
// Loop to print the Fibonacci series
for (int i = 0; i < number; i++) {
System.out.print(fibonacci(i) + " ");
}
}
}
```

**Explanation of the Code**

**Method Definition:**

- public static int fibonacci(int n): This method takes an integer n and returns the nth Fibonacci number.
- Base Cases:

If n is 0, return 0.

If n is 1, return 1. - Recursive Case:

For any other value of n, the method calls itself with n-1 and n-2, and adds the results.

**Main Method:**

- int number = 10;: We want to print the first 10 Fibonacci numbers.
- A for loop iterates from 0 to number – 1 and prints the Fibonacci numbers by calling the fibonacci method.

**How the Recursion Works**

When fibonacci(n) is called:

- If n is 0 or 1, it returns the base case.
- If n is greater than 1, it breaks the problem into smaller subproblems: fibonacci(n-1) and fibonacci(n-2).
- This process continues until it reaches the base cases, and then it combines the results to give the final output.

**Example Execution**

For fibonacci(5):

- It calls fibonacci(4) and fibonacci(3).
- fibonacci(4) calls fibonacci(3) and fibonacci(2).
- This continues until the base cases are reached, and then the results are summed up step by step.

## Fibonacci Series in Java FAQs

### Is IIT Indore a good IIT?

Yes, IIT Indore is considered a good institute known for its quality education and research opportunities.

### What is IIT Indore famous for?

IIT Indore is renowned for its strong academic programs, especially in computer science, electrical engineering, and mechanical engineering.

### Which branch is best in IIT Indore?

The computer science and engineering (CSE) branch is highly regarded at IIT Indore for its excellent faculty and industry connections.

### How can I get 100% scholarship in IIT?

To get a 100% scholarship in IIT, you typically need to excel academically and meet specific criteria set by the institute or external scholarships.

### Do IIT students get scholarships?

Yes, IIT students have access to various scholarships based on merit, financial need, or specific criteria set by the institute or external organizations.

### How much rank is required to get into IIT Indore?

The rank required to get into IIT Indore varies each year but generally falls within the top few thousand ranks in the JEE Advanced exam.

### How many seats are in IIT Indore?

IIT Indore has a limited number of seats available each year, typically around a few hundred across various undergraduate and postgraduate programs.

### How much rank is required for IIT Indore?

Generally, securing a rank within the top few thousand in the JEE Advanced exam is required for admission to IIT Indore.

### What is the lowest package in IIT Indore CSE?

The lowest package in IIT Indore's computer science and engineering (CSE) department varies but is typically competitive compared to other top institutions.

### What rank is needed for IIT Indore?

A rank within the top few thousand in the JEE Advanced exam is generally required for admission to IIT Indore.

### What is the minimum marks to get into IIT Indore?

The minimum marks required to get into IIT Indore depend on various factors, including the difficulty level of the entrance exam and the number of applicants.

### What is the highest package of IIT Indore?

The highest package offered at IIT Indore varies each year but is typically competitive and attractive to students seeking placements.

### Is IIT Indore good for placement?

Yes, IIT Indore has a good placement record with many reputed companies visiting the campus for recruitment across various disciplines.

### What is the highest package in IIT Indore?

The highest package offered at IIT Indore varies each year but is usually substantial, especially for students in sought-after disciplines.

### What is the lowest package of IIT Indore CSE?

The lowest package offered to students in the computer science and engineering (CSE) department at IIT Indore varies but is generally competitive compared to other top institutions.