what is a triangular number

Question

this is how i feel, i have spent half an hour looking for what a triangular number is, please answer

love,

                Holly

Answer 1

A triangular number is the sum of the first n natural numbers, where n is the length of an equilateral triangle. The easiest way to think of a triangular number is to think of a triangular frame containing a number of equal-sized balls. The frame would look like a snooker or pool triangle used to contain a number of balls (6 or 10 for example). The number of balls is a triangular number. They form a sequence:

1, 3, 6, 10, 15, 21, etc.

The formula for generating a triangular number is T_n=n(n+1)/2 where n is the side length of the triangle.