Help me solve this input output table?

Question

1 1
2 3
3 6
4 10
5 15
6 21

So what equation should I do to get from the number in the first column to the number in the second column?

Answer 1

I usually "play aroung" with the y values, I found this ....
suppose we double all y values

1 2 = 1x2
2 6 = 2x3
3 12 = 3x4
4 20 = 4x5
5 30 = 5x6
6 42 = 6x7
...
n ----> n(n+1)
Did you see the pattern ?

but remember we multiplied by 2

so, .....

y = x(x+1)/2