Triangular number

A triangular number is a number that is the sum of all of the natural numbers up to a certain number. When formed using regularly spaced dots, they tend to form a shape of either an equilateral or a right triangle, hence the name.^[1]

The first six triangular numbers

For example, 10 is a "triangular number" because ${\displaystyle 10=1+2+3+4}$.

The first 25 triangular numbers are: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, and so on.

A triangular number is calculated by the equation: ${\displaystyle {\frac {n(n+1)}{2}}}$.