Loading...
Triangle NumbersLoading...
![](https://assets.api.bookcreator.com/LjVJoI41YlQEPvY5bvXuw7UGmuM2/books/VNMPjrTWTBqAiQP37G_F2w/assets/bE7L90B6TjOaKqnI3HUNGQ.png?width=536&height=384)
![](/_next/static/media/shadow-light.2e386fee.png)
![](/_next/static/media/shadow-brighten.a2a9d200.png)
The natural numbers are given by 1, 2, 3, 4, 5, 6, ... etc.
![](https://assets.api.bookcreator.com/LjVJoI41YlQEPvY5bvXuw7UGmuM2/books/VNMPjrTWTBqAiQP37G_F2w/assets/hzx_jZDETkKCGZ0FV80faw.png?width=398&height=427)
1
2
3
4
5
6
The triangle numbers are the sums of the first n natural numbers.
![](https://assets.api.bookcreator.com/LjVJoI41YlQEPvY5bvXuw7UGmuM2/books/VNMPjrTWTBqAiQP37G_F2w/assets/rCxomEbESD2MdDRkumuWbA.png?width=629&height=560)
The triangle numbers Tn are the sums of the first n natural numbers.
![](https://assets.api.bookcreator.com/LjVJoI41YlQEPvY5bvXuw7UGmuM2/books/VNMPjrTWTBqAiQP37G_F2w/assets/rCxomEbESD2MdDRkumuWbA.png?width=629&height=560)
T1 = 1
T2 = 1 + 2
T3 = 1 + 2 + 3
T4 = 1 + 2 + 3 + 4
T5 = 1 + 2 + 3 + 4 + 5
T6 = 1 + 2 + 3 + 4 + 5 + 6
.
.
.
.
.
.
.
.
.
.
etc.
They are so named because they form a triangle of size n.
The tetrahedral numbers are the sums of the first n triangle numbers.
![](https://assets.api.bookcreator.com/LjVJoI41YlQEPvY5bvXuw7UGmuM2/books/VNMPjrTWTBqAiQP37G_F2w/assets/MrxK8f_qRs6hT100-h3XEg:m4v/000.jpg?width=568&height=426)
Challenge [hard]: What comes next?
![](https://assets.api.bookcreator.com/LjVJoI41YlQEPvY5bvXuw7UGmuM2/books/VNMPjrTWTBqAiQP37G_F2w/assets/2zGWkxeZQa6jlX7ueNKokw.png?width=734&height=490)