The answer is $\boxed{175}$.
The sequence is generated by multiplying the previous number by 2 and then subtracting 12. For example, the first number is 90, which is 2 times 45 minus 12. The second number is 180, which is 2 times 90 minus 12. The third number is 12, which is 2 times 6 minus 12. And so on.
The next number in the sequence is 175, which is 2 times 87.5 minus 12.
Here is a table showing the first few numbers in the sequence:
Number | Formula
——- | ——–
90 | 2 * 45 – 12
180 | 2 * 90 – 12
12 | 2 * 6 – 12
50 | 2 * 25 – 12
100 | 2 * 50 – 12
200 | 2 * 100 – 12
175 | 2 * 87.5 – 12
Option A, 150, is not in the sequence because it is not a multiple of 2.
Option B, 175, is in the sequence because it is a multiple of 2 and it is 12 less than the previous number in the sequence.
Option C, 225, is not in the sequence because it is not a multiple of 2.
Option D, 250, is not in the sequence because it is not a multiple of 2 and it is 12 less than the previous number in the sequence.