Triangular number - GCSE Maths Definition

A triangular number is a number, that if drawn as a number of dots (say), can be arranged into a triangle - think of the pack of reds at the start of a frame of snooker.

Triangular numbers are built up from an easy to see pattern

• the first triangular number is 1
  (that first red just above the pink spot in snooker)

• the second triangular number is 1 + 2 = 3
  (the first two rows of reds at the start of a frame of snooker)

• the third would be 1 + 2 + 3 = 6

(For completeness, there are five rows of reds at the start of a frame of snooker, giving 1 + 2 + 3 + 4 + 5 = 15 reds).

This leads to the general case that the triangular numbers come from adding the natural numbers (1, 2, 3, 4, ...) together. A shortcut formula for the n^th triangular number is