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?
denotes the set of elements in both A and C, which is
.
denotes the complement of set B, which is the set of all elements that are in the universal set that are not in set B. In this case, this set is