### Instruction: What is the 100th letter in the pattern ABCABCABC...?### Response: I notice that the pattern repeats every three letters, so I can use modular arithmetic to find the position of the 100th letter within the cycle.
If I divide 100 by 3, I get a quotient of 33 and a remainder of 1.
This means that the 100th letter is the same as the first letter in the cycle, which is A.