Triangular Numbers

triangular-number-10A triangular number correspond to the number of dots that would appear in an equilateral triangle when using a basic triangular pattern to build the triangule.

The triangular numbers sequence contains all the triangular numbers in order.

The first 10 numbers of the triangular number sequence are:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …

trinagular-number-sequence

The following table shows how we can calculate each triangular number from this sequence:

Triangular Number Calculation
1 =1
3 =1+2
6 =1+2+3
10 =1+2+3+4
15 =1+2+3+4+5

So using an iterative approach in Python we can easily write a script to work out the first 100 triangular numbers:

This short program is a good example of:
iteration-label

Finding the nth term in the sequence


THe following mathematical formula can be used to find the nth triangular number in this sequence:

nth term = n(n+1)/2

Other Number Sequences


The following Python challenges will get you to work with different types of number sequences and series:

Series vs. Sequence?


Did you know?
The main difference between a series and a sequence is that a series is the sum of the terms of a sequence.
So let’s investigate the following Python challenges based on series:

Extra Challenge


You may also enjoy the following challenge:

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