What is the next number in the sequence: 2, 6, 12, 20, ...?

To determine the next number in the sequence 2, 6, 12, 20, it's important to identify the pattern among the numbers.

First, observe the differences between consecutive terms:

• 6 - 2 = 4

• 12 - 6 = 6

• 20 - 12 = 8

The differences between the terms form the sequence 4, 6, and 8. Noticing this, we can see that these differences increase by 2 each time. This leads us to deduce that the next difference should be 10 (since 8 + 2 = 10).

Adding this next difference to the last number in the original sequence:

20 + 10 = 30.

Thus, the next number in the sequence is 30, which aligns with the identified pattern of increasing differences. This method of recognizing a pattern in the differences is commonly used in number sequences.