Question

What are triangular numbers?

Answer 1

Triangular numbers

A triangular number sequence $T_n$ is a number represented by dots arranged in an equilateral triangle.

The numbers$1,3,6,10,15,$ and so on are the numbers in the triangular series.

Each triangle builds on the preceding one by adding a bottom row of dots with one more dot than the previous bottom row.

The $T_n$ denotes the $n^{th}$ triangular number as :

$T_n=1+2+3+...+n$

The triangular dot pattern is shown below:

Thus, a triangular number $T_n$ is a number that can be represented by dots arranged in an equilateral triangle.