Step-by-step Solution:

The series is 1, 7, 15, 25, 37, ...

Differences between consecutive terms:

• 7 - 1 = 6
• 15 - 7 = 8
• 25 - 15 = 10
• 37 - 25 = 12

The differences increase by 2 each time, so the next difference is 12 + 2 = 14.

The next term is 37 + 14 = 51.

Answer: (D) 51