// CSC 240 - Diagnostic Q1 - Gauss Sum (CSC 141, loops)
// Sum 81297 + 81495 + 81693 + ... + 100899  (each step adds the same amount).
public class Q1_GaussSum {
    public static void main(String[] args) {
        int start = 81297;
        int end   = 100899;
        int step  = 198;        // ANSWER 1: common step between terms

        // ANSWER 2: number of terms = (end - start) / step + 1
        int terms = (end - start) / step + 1;
        System.out.println("Number of terms = " + terms);   // 100

        // ANSWER 3: the loop that accumulates the sum
        long sum = 0;           // long is safest; here 9.1M fits an int too
        for (int v = start; v <= end; v += step) {
            sum += v;
        }
        System.out.println("Sum = " + sum);                 // 9109800

        // Cross-check with Gauss's formula: terms * (first + last) / 2
        long check = (long) terms * (start + end) / 2;
        System.out.println("Formula check = " + check);     // 9109800
    }
}