The series follows the pattern of doubling the previous term and adding 1, or alternatively, the terms are 2^(n+1) - 1. For the last term, 63 * 2 + 1 = 127.
The pattern in this series is that each number is multiplied by 2 and then 1 is added to find the next number. For example, 3 times 2 plus 1 is 7, 7 times 2 plus 1 is 15, and 31 times 2 plus 1 is 63. Applying this same logic to the last term, 63 times 2 plus 1 equals 127.