TheAlgorithms-C/project_euler/problem_1/sol2.c

/**
 * \file
 * \brief [Problem 1](https://projecteuler.net/problem=1) solution
 *
 * If we list all the natural numbers below 10 that are multiples of 3 or 5,
 * we get 3,5,6 and 9. The sum of these multiples is 23.
 * Find the sum of all the multiples of 3 or 5 below N.
 *
 * This solution is based on the pattern that the successive numbers in the
 * series follow: 0+3,+2,+1,+3,+1,+2,+3.
 */
#include <stdio.h>

/** Main function */
int main()
{
    int n = 0;
    int sum = 0;
    scanf("%d", &n);

    int terms = (n - 1) / 3;
    sum += ((terms) * (6 + (terms - 1) * 3)) / 2;  // sum of an A.P.
    terms = (n - 1) / 5;
    sum += ((terms) * (10 + (terms - 1) * 5)) / 2;
    terms = (n - 1) / 15;
    sum -= ((terms) * (30 + (terms - 1) * 15)) / 2;

    printf("%d\n", sum);
}