Question

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 1

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

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.