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.

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.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

table a is wierd

step-by-step explanation:

6*f