Final answer:
To find the next number in the sequence, a pattern in the differences between terms was observed, alternating between adding 1 and adding 3 to the previous difference. Following this pattern, the next number after 63 is 68, making the correct answer D) 68.
Step-by-step explanation:
The sequence provided is: 53, 56, 57, 61, 63, ... We need to determine the next number. Looking at the differences between consecutive terms, we have the following sequence of differences: 3, 1, 4, 2. This appears to follow a pattern where each difference alternates between adding 1 and adding 3 (3 = 1 + 2, 1 = 3 - 2, 4 = 1 + 3, 2 = 4 - 2). If this pattern continues, the next difference would be adding 3 to the last difference, so the next difference would be 2 + 3 = 5.
Thus, the next number in the original sequence after 63 would be 63 + 5 = 68.
The correct answer is D) 68.