What is the next number in the sequence 3, 7, 15, 31, 63?

In this sequence, each number can be identified as one less than a power of 2. Specifically:

• The first number is 3, which is equal to (2^2 - 1) (4 - 1).

• The second number is 7, which is equal to (2^3 - 1) (8 - 1).

• The third number is 15, which is equal to (2^4 - 1) (16 - 1).

• The fourth number is 31, which is equal to (2^5 - 1) (32 - 1).

• The fifth number is 63, which is equal to (2^6 - 1) (64 - 1).

Continuing this pattern, the next number in the sequence should be one less than (2^7). Calculating (2^7) gives us 128. Therefore, one less than 128 is 127.

This understanding of the progression helps identify 127 as the next number in the sequence, confirming the accuracy of the chosen answer.