# 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.

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