Generic triangular numbers sequence formula

I know that I can get the nth element of the following sequence

1   3   6  10  15  21

With the formula

(n * (n + 1)) / 2

where n is the nth number I want. How can I generalise the formula to get the nth element of the following sequences where by following sequences I mean

1 -> 1   3   6   10  15  21
2 -> 2   5   9   14  20
3 -> 4   8   13  19
4 -> 7   12  18
5 -> 11  17
6 -> 16