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

To identify the next number in the sequence 3, 7, 15, 31, 63, it is helpful to look for a pattern. Observing the relationship between the numbers reveals that each subsequent number can be derived from the previous number by a specific mathematical operation.

Starting from the first number, if you analyze how each term relates to the next, you can see the following:

• The second number, 7, can be generated from 3 by using the formula: (3 \times 2 + 1 = 7).

• For the third number, you apply the same logic: (7 \times 2 + 1 = 15).

• Continuing this pattern for the fourth number, (15 \times 2 + 1 = 31).

• Finally, for the fifth number, (31 \times 2 + 1 = 63).

This relationship suggests that each number in the sequence can be formulated as:

[ \text{Next number} = \text{Previous number} \times 2 + 1 ]

To find the next number after 63, we continue applying the established formula:

[ 63 \times 2 + 1