Triangular Number Sequence
This is the Triangular Number Sequence:
|1, 3, 6, 10, 15, 21, 28, 36, 45, ...|
This sequence is generated from a pattern of dots which form a triangle.
By adding another row of dots and counting all the dots we can find the next number of the sequence:
We can make a "Rule" so we can calculate any triangular number.
First, rearrange the dots (and give each pattern a number n), like this:
Then double the number of dots, and form them into a rectangle:
- The rectangles are n high and n+1 wide
- and xn is how many dots in the triangle (the value of the Triangular Number n)
And we get (remembering we doubled the dots):
Rule: xn = n(n+1)/2
Example: the 5th Triangular Number is
x5 = 5(5+1)/2 = 15
Example: the 60th is
x60 = 60(60+1)/2 = 1830
Wasn't it much easier to use the formula than to add up all those dots?