Given sequence: 4, 15, 63, 247, 995

To find the pattern in the sequence, let's analyze the differences between consecutive terms:

15 - 4 = 11
63 - 15 = 48
247 - 63 = 184
995 - 247 = 748

From the differences, we can observe that they are increasing in a pattern:

11, 48, 184, 748

This new sequence of differences is not immediately recognizable, so let's analyze the differences between these differences:

48 - 11 = 37
184 - 48 = 136
748 - 184 = 564

Again, we can observe that these differences are increasing in a pattern:

37, 136, 564

Now, let's analyze the differences between these second-level differences:

136 - 37 = 99
564 - 136 = 428

These differences do not appear to follow a specific pattern.

Therefore, we can conclude that the given sequence follows a pattern where the differences between consecutive terms increase in a pattern, but the differences between the second-level differences do not follow a specific pattern.

To find the next term in the sequence, we need to continue the pattern with the increasing differences between consecutive terms:

564 + 428 = 992

Now, we can find the next term in the original sequence by adding the last difference to the previous term:

995 + 992 = 1987

Therefore, the next term in the sequence is 1987.

None of the given options match 1987. However, option D (3971) is the closest to 1987, with only a difference of 16. So, option D (3971) is the correct answer.