This is fairly simple actually:
There are 67 terms in the sequence: floor((321-123)/3) + 1 = 67
The sequence starts at 123
The sequence ends at 321: 3 * floor((321-123)/3) + 123
The average term is (123 + 321) / 2 = 222
The total is going to be average term * number of terms = 222 * 67 = 14874
I've verified this total with a small piece of Java code that doesn't take the above shortcut:
Code:
long sum = 0;
for (long test = 123; test <= 321; test += 3) {
sum += test;
}
System.out.println("sum = " + sum);