In the given pattern of the sum of numbers the results 6, 9 and 12.
Let us check what number should be added with 6 to get 9 and 9 to get 12.
6 + 3 = 9,
9 + 3 = 12
So, each number when added to 3 gives the next number.
Hence, the resulting numbers in the pattern increase by 3.