Triangular Number Sequence
This is the Triangular Number Sequence:
<span>1, 3, 6, 10, 15, 21, 28, 36, 45, ...</span>
This sequence comes from a pattern of dots that form a triangle:
By adding another row of dots and counting all the dots we can
find the next number of the sequence.
A Rule
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:
<span><span>The rectangles are n high and n+1 wide</span><span>and <span>xn</span> is how many dots in the triangle (the value of the Triangular Number n)</span></span>
And we get (remembering we doubled the dots):
<span>2xn = n(n+1)</span><span>xn = n(n+1)/2</span>
<span>Rule: xn = n(n+1)/2</span>
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?
