C Program to Find the Sum of Fibonacci Numbers at Even Indexes up to N Terms

The Fibonacci sequence starts with 0, 1, and each subsequent number is the sum of the previous two numbers. The task is to find the sum of Fibonacci numbers present at even indexes from 0 to 2N.

Fibonacci Sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

Example:

For N = 5, the even indexes are 0, 2, 4, 6, 8, 10.

Therefore:

F(0) + F(2) + F(4) + F(6) + F(8) + F(10)
= 0 + 1 + 3 + 8 + 21 + 55
= 88

Approach

Generate the Fibonacci sequence up to index 2N and add the numbers whose indexes are even.

• Initialize the first two Fibonacci numbers as 0 and 1.
• Generate Fibonacci numbers up to index 2N.
• Add the Fibonacci number whenever its index is even.
• Return the calculated sum.

#include <stdio.h>

// Calculates the sum of Fibonacci numbers at even indexes
int calculateEvenSum(int n)
{
    if (n < 0)
        return 0;

    int fibo[2 * n + 1];

    // Initialize the first two Fibonacci numbers
    fibo[0] = 0;
    fibo[1] = 1;

    int sum = fibo[0];

    // Generate Fibonacci numbers up to index 2n
    for (int i = 2; i <= 2 * n; i++) {
        fibo[i] = fibo[i - 1] + fibo[i - 2];

        // Add Fibonacci numbers at even indexes
        if (i % 2 == 0)
            sum += fibo[i];
    }

    return sum;
}

int main()
{
    int n = 5;

    // Calculate the sum of even-indexed Fibonacci numbers
    int sum = calculateEvenSum(n);

    printf("Sum of Fibonacci numbers at even indexes = %d", sum);

    return 0;
}

Sum of Fibonacci numbers at even indexes = 88

Explanation

• The array stores Fibonacci numbers from index 0 to 2n.
• The loop generates each Fibonacci number using the previous two values.
• Fibonacci numbers at even indexes are added to sum.