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

Here, we will build a C Program to Find the Sum of Fibonacci numbers at even indexes up to N terms

Fibonacci Numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……

Input: 

N = 5

Output:

88 // Sum of the elements at even indexes = 0 + 1 + 3 + 8 + 21 + 55 = 88

Approach:

This approach includes solving the problem directly by finding all Fibonacci numbers till 2n and adding up only the even indices numbers from the array. 

Example:

C

// C Program to find the sum of
// even-indices Fibonacci numbers
#include <stdio.h>

// Computes value of the first
// fibonacci numbers and stores
// the even-indexed sum
int calculateEvenSum(int n)
{
    // return 0 if n is equals or less than to 0
    if (n <= 0)
        return 0;

    int fibo[2 * n + 1];
    fibo[0] = 0, fibo[1] = 1;

    // Initialize the result
    int sum = 0;

    // Adding the remaining terms
    for (int i = 2; i <= 2 * n; i++) {
        fibo[i] = fibo[i - 1] + fibo[i - 2];

        // For even indices
        if (i % 2 == 0)
            sum += fibo[i];
    }

    // Return alternating sum
    return sum;
}

// Driver Code
int main()
{

    // Get n
    int n = 5;

    // calculateEvenSum(n) function is computed and return
    // the sum of even-indices Fibonacci numbers.
    int sum = calculateEvenSum(n);

    // display result
    printf("Even indexed Fibonacci Sum upto %d terms = %d",
           n, sum);

    return 0;
}

Output

Even indexed Fibonacci Sum upto 5 terms = 88

Time Complexity: O(N)

Space Complexity: O(1)