Question

What is triangular number and sequence?

Answer 1

Triangular numbers and sequences:

• The depiction of numbers in the form of an equilateral triangle arranged in a series or sequence is known as the triangular number sequence. The numerals are arranged in the following order: $1,3,6,10,15,21,28,36,45,$ and so on.
• Dots represent the numbers in the triangular design.

• A three-dimensional number ${\mathrm{T}}_{\mathrm{n}}$ is a metaphorical number that can be represented as an equilateral triangular grid of elements with each row containing one more element than the preceding one.
• The numbers are:$$\begin{gathered} 0,1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136, \\ 153,171,190,210,231,253,276,300,325,351,378,406,435, \\ 465,496,528,561,595,630,666,703,741,780,820,861,903, \\ 946,990,1035,1081,1128,1176,1225,1275,1326,1378,1431, \end{gathered}$$and so on.