What are triangular numbers?

The Triangle numbers are special numbers that follow a specific pattern.

Answer: Triangular numbers are the ones that give a triangular pattern and for a given number n, the triangular number is n(n + 1)/2.

Let's look into some examples to understand triangle numbers.

Explanation:

Triangular numbers are the ones that form a triangular dot pattern. 1, 3, 6, 10, 15 are triangular numbers as shown below:

Triangular numbers can be found by Faulhaber’s formula: T_n = [ n (n + 1) ] / 2

• n = 1 ⇒ T_n = 1(1 + 1)/2 = 1(2)/2 = 1 dot
• n = 2 ⇒ T_n = 2(2 + 1)/2 = 2(3)/2 = 3 dots
• n = 3 ⇒ T_n = 3(3 + 1)/2 = 3(4)/2 = 6 dots

These triangle numbers form equilateral triangles.

Therefore, the triangular numbers are the ones that give a triangular pattern and for a given number n, the triangular number is n(n + 1)/2.