The pattern here is that for each number, they are adding 1 more than they added to the previous number. We can see this because they add 1 and 2 to make 3, 3 and 3 to make 6, 6 and 4 to make 10, and 10 and 5 to make 15.
With this logic, we know the next number in the pattern is 21 because 15+6 is 21.
