The Fibonacci series is a sequence of numbers where each number is the sum of the two preceding ones, typically starting with 0 and 1. The series goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

Fibonacci Series Formula

The Fibonacci sequence can be defined recursively as follows:

• F(0) = 0
• F(1) = 1
• F(n) = F(n-1) + F(n-2) for n > 1

Implementation in C

You can implement the Fibonacci series in C using either recursion or iteration. Below are examples for both methods.

Example 1: Fibonacci Series Using Iteration

#include <stdio.h>

void fibonacciIterative(int n) {
    int first = 0, second = 1, next;

    printf("Fibonacci Series (Iterative):\n");
    printf("%d, %d", first, second); // Print the first two numbers

    for (int i = 2; i < n; i++) {
        next = first + second; // Calculate the next number
        printf(", %d", next); // Print the next number
        first = second; // Update first to the previous second
        second = next; // Update second to the newly calculated number
    }
    printf("\n");
}

int main() {
    int n;

    printf("Enter the number of terms in Fibonacci Series: ");
    scanf("%d", &n);
    fibonacciIterative(n); // Call the function
    return 0;
}

Explanation:

• The fibonacciIterative function computes the Fibonacci series iteratively.
• It starts by initializing the first two numbers (0 and 1) and then calculates the next numbers in the series using a loop.
• The loop continues until the desired number of terms is reached.

Example 2: Fibonacci Series Using Recursion

#include <stdio.h>

// Recursive function to calculate Fibonacci number
int fibonacciRecursive(int n) {
    if (n == 0) return 0; // Base case
    if (n == 1) return 1; // Base case
    return fibonacciRecursive(n - 1) + fibonacciRecursive(n - 2); // Recursive call
}

void printFibonacciRecursive(int n) {
    printf("Fibonacci Series (Recursive):\n");
    for (int i = 0; i < n; i++) {
        printf("%d, ", fibonacciRecursive(i)); // Print Fibonacci number at position i
    }
    printf("\n");
}

int main() {
    int n;

    printf("Enter the number of terms in Fibonacci Series: ");
    scanf("%d", &n);
    printFibonacciRecursive(n); // Call the function
    return 0;
}

Explanation:

• The fibonacciRecursive function calculates the Fibonacci number for a given position using recursion.
• The printFibonacciRecursive function prints the Fibonacci series by calling the recursive function for each term.
• The base cases handle the first two numbers of the Fibonacci sequence.

Output Example

For both implementations, if you enter 10 when prompted, the output will be:

Fibonacci Series (Iterative):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34

Fibonacci Series (Recursive):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34,

Summary

• The Fibonacci series is a classic example of a sequence defined recursively.
• It can be implemented in C using either iterative or recursive methods.
• The iterative approach is generally more efficient than the recursive one, especially for larger terms, as it avoids the overhead of multiple function calls and reduces redundant calculations.