Reiny (this was the one you helped me with)
posted by Keira .
I tried to explain it by using the arrangement of billiard balls, but I guess you don't play pool.
let me try to "draw" the billiard balls
. . .o
. . o o
. .o o o
. o o o o
o o o o o o
sum of one row = 1
sum of two rows = 3
sum of three rows = 6
sum of four rows = 10
sum of five rows = 15
difference between first and second = 2
difference between third and second = 3
difference between fourth and third = 4
difference between fifth and fourth = 5
Can you now continue the pattern?
They are called the "triangular" numbers since they form an equilateral triangle.
here is another pattern for your third column numbers
1 = (2x1)/2
3 = (3x2)/2
6 = (4x3)/2
nth number = (n+1)(n)/2