This series follows a pattern where each term is multiplied by 2 and then 1 is added to find the next term. Multiplying 3 by 2 and adding 1 gives 7, multiplying 7 by 2 and adding 1 gives 15, and multiplying 15 by 2 and adding 1 gives 31. Applying this rule to 31, we multiply by 2 and add 1 to arrive at 63.