The triangle
numbers are the numbers in the sequence

1, 3, 6, 10, 15, 21, 28, 36,............., 1/2 n (n + 1)

Where n is any whole number, and are so called because they correspond
to the numbers of dots required to build shapes.

It can be seen
that each new triangle is formed from the previous triangle by adding
a new base with one more dot than the previous base. Each triangle
number is the sum of consecutive whole numbers, for example the
fifth number is

1 + 2 + 3 + 4 + 5 = 15.