To find the missing number in the given sequence, let's observe the pattern between the numbers:
361, 289, _______, 169, 121
By looking at the given numbers, we can see that each number is the square of a certain value:
19^2 = 361
17^2 = 289
13^2 = 169
11^2 = 121
Therefore, the missing number should be the square of the next smaller number, which is 15:
15^2 = 225
So, the missing number in the sequence is 225.
The correct answer is option F) 225.