To find the pattern in the given sequence, let's look at the differences between consecutive terms:
1, 2, 4, 13, 31, 112
The differences are:
1, 2, 9, 18, 81
Looking closely at the differences, we can see that they are increasing by a factor of 2 each time. Specifically, the differences are:
2 - 1 = 1
9 - 2 = 7
18 - 9 = 9
81 - 18 = 63
Now, let's add these differences to the previous term to get the next term in the sequence:
1 + 1 = 2
2 + 7 = 9
9 + 9 = 18
18 + 63 = 81
Adding these terms to the previous terms, we get the following sequence:
1, 2, 4, 13, 31, 112, 224
Therefore, the correct answer is B) 224.