12,9,3,6,3,1

The sequence provided is 12, 9, 3, 6, 3, 1. Analyzing the differences between consecutive terms:

1. 12 → 9: Subtract 3

2. 9 → 3: Subtract 6

3. 3 → 6: Add 3

4. 6 → 3: Subtract 3

5. 3 → 1: Subtract 2

The operations sequence is -3, -6, +3, -3, -2. Observing the absolute values of these operations: 3, 6, 3, 3, 2, there appears to be a gradual reduction in the subtraction magnitude. Following this trend, the next operation might involve subtracting 1 (continuing the decrease from 2).

Next term: (1

Answer: The next number in the sequence is 0.

boxed{0}