# Strange equation

• Sep 21st 2005, 09:58 AM
vab123
Strange equation
I have come across this equation in a puzzle and I don't even know what it is, never mind the answer. Can any one help me, please?
Here it is: -

sum = 0
Do n = 123 To 321 Step 3
sum = sum + n
Loop n
Display sum
• Sep 21st 2005, 11:17 AM
rgep
It's asking for the sum 123 + 126 + 129 + ... + 312.
• Sep 21st 2005, 11:27 AM
vab123
Strange equation
Thank you for your help. When I'm faced with equations like that I think my mind just shuts down.
• Oct 28th 2005, 01:21 PM
Gamigin
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);```