Printing the sums of numbers from 1 to 10 with only 1 loop
Yes, it is possible.

public static void printSums() {
    int sum = 0;
    for (int i = 1; i &lt;= 10; i++) {
        sum += i;
        System.out.println(sum);
    }
}


The key is simply to calculate the sum of the first \$N\$ digits. It is easy if you already have the sum of the first \$N-1\$ digits : you simply add \$N\$.