Calculate the nth triangular number. A triangular number counts the objects that can form an equilateral triangle. The nth triangular number is the number of dots composing a triangle with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n.

Answer: Xn = n (n+1) / 2

Step-by-step explanation:

Firstly, you work with asingle dot for each and let n = 1,2,3,4 ...

Now if you double the dots, it will form a rectangle and it is easier to work with many dots i. e just multiple n by n+1

Dots in rectangle = n (n+1)

But remember the number of dots were doubled therefore,

Dots in triangle = n (n+1) / 2.