Last Updated on July 3, 2024 by Abhishek Sharma

The Fibonacci sequence is named after the Italian mathematician Leonardo Fibonacci, who lived in the early thirteenth century. In this sequence, each number is the sum of the two preceding numbers. The sum of the first two elements in the sequence equals the next element.

The first two numbers in the Fibonacci sequence must either be 1 and 1 or 0 and 1, depending on the chosen starting point, and each consecutive number must be the sum of the two before it.

## What is Fibonacci Series?

Any number in the series can be calculated as the direct sum of the two numbers before it.

Following is Fibonacci Series –

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

### How does the Fibonacci Sequence Function?

The following number in the Fibonacci sequence is determined by adding the two numbers before it. The numbers 0 and 1 are the first two of a Fibonacci sequence.

The function gives a mathematical definition of the Fibonacci number series Fn.

`Fn=Fn-1 + Fn-2`

Using the values of the first two terms,

`F0 = 0 and F1 = 1`

The Fibonacci series begins as follows.

`0,1,1,2,3,5,8,13,21,........`

**In two ways Fibonacci series can be written –**

- Fibonacci series without recursion
- Fibonacci series using recursion

### Method 1 of the Fibonacci Series Without Recursion ( Iterative Approach)

Fibonacci sequences avoid using recursion and instead use two variables, f1, and f2, with starting values of 0 and 1, respectively, to represent the first and second components of the Fibonacci sequence.

Print f2 after iterating from 1 to n-1, then save it in a temporary variable and update f2 with f2 + f1 and f1 as f2.

**Code Implementation**

#include <bits/stdc++.h> using namespace std; int main() { int number = 7; int f1=0,f2=1,f3; cout<<f1<<" "<<f2<<" "; for(int i=2;i<number;i++) { f3=f1+f2; cout<<f3<<" "; f1=f2; f2=f3; } return 0; }

**Output**

`0 1 1 2 3 5 8`

**Time Complexity :** O(n)

**Space Complexity :** O(1)

### Method 2 of the Fibonacci Series Using Recursion

Steps to build the Fibonacci series using recursion:

Create a recursive function with an integer parameter N.

- The Fibonacci number will be zero if N = 0.
- Otherwise, if n=1 The first Fibonacci number is 1.
- If not, func(n-1) + func(n-2) return value.

**Code Implementation**

#include <bits/stdc++.h> using namespace std; int fibonacci_series(int n) { if(n == 0){ return 0; } else if(n == 1){ return 1; } else{ return fibonacci_series(n-2) + fibonacci_series(n-1); } } int main() { int n = 7; for(int i = 0; i < n; i++) { cout << fibonacci_series(i) << " "; } return 0; }

**Output**

`0 1 1 2 3 5 8`

**Time Complexity :** O(n*2^n)

**Space Complexity :** O(n) ( Recursion stack space)

**Conclusion**

In conclusion, the Fibonacci series is a fascinating sequence of numbers with applications in various fields such as mathematics, computer science, and nature. Printing the Fibonacci series up to N numbers is a common programming exercise that helps develop a deeper understanding of iterative and recursive algorithms. By implementing both methods in C, one can gain insights into the efficiency and performance differences between iterative and recursive approaches. Understanding and coding the Fibonacci series is an essential step in learning how to solve problems using basic programming concepts and techniques.

## Frequently Asked Questions related to C Program to Print Fibonacci Series up to N Numbers

Here are some of the FAQs related to C Program to Print Fibonacci Series up to N Numbers

**1. What is the Fibonacci series?**

The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence goes 0, 1, 1, 2, 3, 5, 8, and so on.

**2. How can I write a C program to print the Fibonacci series up to N numbers?**

You can write a C program to print the Fibonacci series up to N numbers using either an iterative approach or a recursive approach. The iterative approach uses loops, while the recursive approach involves calling a function that calls itself.

**3. What is the difference between iterative and recursive methods in C?**

The iterative method uses loops to repeat a set of instructions until a condition is met. The recursive method involves a function calling itself with modified parameters until a base condition is reached. Iterative methods are usually more efficient in terms of memory and speed compared to recursive methods, which can be easier to understand and implement for certain problems.

**4. Why might I choose an iterative method over a recursive method to print the Fibonacci series?**

You might choose the iterative method over the recursive method because it is generally more efficient in terms of memory usage and execution speed. Recursive methods can lead to stack overflow if the recursion depth is too large, which is not a concern with iterative methods.

**5. Can the Fibonacci series be generated without using loops or recursion?**

Yes, the Fibonacci series can also be generated using matrix exponentiation or Binet’s formula, which involves mathematical expressions. However, these methods are less common for basic programming exercises.