Pattern Analysis:

To find the missing number in the sequence 1, 3, 15, 55, ?, 899, we need to identify the pattern or relationship between the given numbers.

First Difference:
Let's calculate the first differences between consecutive terms in the sequence:

3 - 1 = 2
15 - 3 = 12
55 - 15 = 40
? - 55 = x
899 - ? = y

Second Difference:
Now, let's calculate the second differences between the first differences:

12 - 2 = 10
40 - 12 = 28
x - 40 = z
y - x = w

Third Difference:
Finally, let's calculate the third differences between the second differences:

28 - 10 = 18
z - 28 = p
w - z = q

Identifying the Pattern:
From the calculations above, we can observe the following pattern:

First Difference: 2, 12, 40, x, y
Second Difference: 10, 28, z, w
Third Difference: 18, p, q

The first difference is increasing by multiples of 6 (2 * 3), and the second difference is increasing by multiples of 8 (4 * 2). Therefore, we can conclude that the third difference should increase by multiples of 10 (5 * 2).

Solving for the Missing Number:
Using the pattern, we can calculate the missing values:

First Difference: 2, 12, 40, 90, 170
Second Difference: 10, 28, 58, 100
Third Difference: 18, 38, 62

Adding the third difference to the last known second difference (100 + 62), we get 162. Adding this value to the last known first difference (170 + 162), we get the missing number:

170 + 162 = 332

Therefore, the missing number in the sequence 1, 3, 15, 55, ?, 899 is 332.

Final Answer:
The correct answer is option 'B' (227).