Which number is the next logical number in the following sequence of numbers 2, 6, 14, 30?

To find the next number in the sequence 2, 6, 14, 30, we need to look for a pattern in the differences between the numbers.

First, let’s examine the differences:

• 6 – 2 = 4
• 14 – 6 = 8
• 30 – 14 = 16

The differences between the numbers are 4, 8, and 16. We can see that these numbers are doubling each time:

• 4 is 2 × 2
• 8 is 2 × 4
• 16 is 2 × 8

If we follow this pattern, the next difference would be 32 (which is 2 × 16).

Now, we take the last number in the sequence, 30, and add 32:

30 + 32 = 62.

Therefore, the next number in the sequence is 62.