Triangular numbers are a sequence of numbers that represent the total dots or points in triangular grids. The first triangular number is 1, as it represents a single dot. Each subsequent triangular number is calculated by adding the previous number to the number of dots in the new row. For example, the second triangular number is 3, representing 1 dot in the first row and 2 dots in the second row. More formally, the nth triangular number can be calculated as n(n+1)/2, where n is the term number. This formula allows calculating any triangular number by multiplying the term number by itself, adding 1, and dividing by 2.

1. TRIANGULAR NUMBERS
ALAN S. ABERILLA

2. The triangular number is a figurate number that can be
represented in the form of a triangular grid of points where
the first row contains a single element and each subsequent
row contains one more element than the previous one.
More formally, a triangular number is a number obtained by
adding all positive integers less than or equal to a given
positive integer n.
It is simply the number of dots in each triangular pattern:
Thus, the triangular
number is sequence is
1, 3, 6, 10, 15, . . .

3. By adding another row of dots and counting all the dots we
can
find the next number of the sequence.
The first triangle has just one dot.
The second triangle has another row with 2 extra dots,
making 1 + 2 = 3
The third triangle has another row with 3 extra dots, making
1 + 2 + 3 = 6
The fourth has 1 + 2 + 3 + 4 = 10
etc!

4. How may dots in the 60th triangle?
A Rule
We can make a "Rule" so we can calculate any triangular number.
First, rearrange the dots like this:

5. Then double the number of dots, and form them into a rectangle:
Now it is easy to work out how many dots: just multiply n by n+1
Dots in rectangle = n(n+1)
But remember we doubled the number of dots, so
Dots in triangle = n(n+1)/2
We can use xn to mean "dots in triangle n", so we get the rule:
Rule: xn = n(n+1)/2

7. ACTIVITY 7:
How many dots in the 10th and 15th triangle?
Solve it through rectangular pattern and double
check it using the formula.
Use short bond paper (handwritten or
computerized) – utilize the folder of assignment
1
triangle