Triangular Numbers Calculator
Use our triangular numbers calculator to calculate triangular numbers instantly. Includes what is a triangular number, how do you get triangular numbers, the triangular number formula, examples, and how to determine if a number is a triangular number.
What is a Triangular Number?
A triangular number is the total number of dots you can arrange in an equilateral triangle. It’s the sum of the first n natural numbers: 1 + 2 + 3 + ... + n.
If you’re asking how do you get triangular numbers, you generate them by adding the next counting number each time: 1, 3, 6, 10, 15, 21, ...
Triangular numbers appear in number patterns, counting problems, and sequences. This triangular numbers calculator finds the triangular number at position n quickly.
Triangular Number Formula
The nth triangular number is the sum of the first n integers. There’s also a closed-form triangular number formula that makes it fast to compute.
This is the definition of triangular numbers.
This is the standard formula for triangular numbers.
So the 7th triangular number is 28.
This helps explain how to find the next triangular number.
How to Use the Triangular Numbers Calculator
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Enter the position n in the triangular number sequence.
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The calculator uses the triangular number formula Tₙ = n(n + 1) / 2.
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Read the result as the triangular number at position n.
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To find the next triangular number, increase n by 1 and calculate again.
Frequently Asked Questions
A triangular number is the sum of the first n natural numbers and represents dots that can form a triangle: Tₙ = 1 + 2 + ... + n.
Use the triangular number formula: Tₙ = n(n + 1) / 2.
Start with 1 and keep adding the next integer: 1, 3, 6, 10, 15, 21, ...
Pick n and compute Tₙ = n(n + 1) / 2, or build the sequence by cumulative sums.
If you have Tₙ, then the next one is Tₙ + (n + 1). Example: T₅=15, so T₆=15+6=21.
Look for the pattern of adding consecutive integers, or use Tₙ = n(n+1)/2 to jump directly to the nth term.
A number x is triangular if 8x + 1 is a perfect square. If √(8x+1) is an integer, then x is a triangular number.
Infinitely many. For every n ≥ 1, there is a triangular number Tₙ.
Tₙ = n(n + 1) / 2.