Triangular number facts for kids
A triangular number is a special kind of number. Imagine you have a bunch of small pebbles or dots. If you can arrange these dots to form a perfect triangle, then the total number of dots you used is a triangular number!
It's also the sum of all the natural numbers up to a certain point. Natural numbers are the counting numbers: 1, 2, 3, 4, and so on. For example, the number 10 is a triangular number because if you add 1 + 2 + 3 + 4, you get 10.
What Are Triangular Numbers?
Triangular numbers get their name because they can be shown as dots arranged in the shape of an equilateral triangle. Each new row in the triangle has one more dot than the row before it.
- The first triangular number is 1 (just one dot).
- The second is 3 (1 + 2 dots).
- The third is 6 (1 + 2 + 3 dots).
- The fourth is 10 (1 + 2 + 3 + 4 dots).
How to Calculate Them
You don't have to add up all the numbers every time! There's a cool math trick, or formula, to find any triangular number. If you want to find the triangular number for a certain number 'n' (like the 5th or 10th triangular number), you use this equation:
Let's try an example. To find the 4th triangular number (where n = 4):
- First, add 1 to n: 4 + 1 = 5
- Next, multiply n by that result: 4 * 5 = 20
- Finally, divide by 2: 20 / 2 = 10.
So, the 4th triangular number is 10, which matches our example above!
List of Triangular Numbers
Here are the first few triangular numbers. See if you can spot the pattern and how they grow!
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300.
