Posted by **Keira** on Saturday, June 27, 2009 at 11:41am.

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

ahhh!

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

10 =(5x4)/2

.

.

nth number = (n+1)(n)/2

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