Triangular Number
Number that we obtain by adding the first n non-zero whole numbers.
Figurate number that can be represented by a triangle or a sequence of interlocked triangles.
The sequence of triangular numbers is: 1, 3, 6, 10, 15, ....[latex]\dfrac {n\left( n+1\right) } {2}[/latex] where [latex]n[/latex] represents both the rank of the term in the sequence and the number of points on the largest triangle in the figure.
- The nth triangular number represents the sum of the first n non-zero whole numbers.
- The sequence of triangular numbers is an infinite sequence: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, ...
Examples
- The number 10 is a triangular number because: 1 + 2 + 3 + 4 = 10.
- The number 21 is a triangular number because: 1+ 2 + 3 + 4 + 5 + 6 = 21.