Triangular Numbers

A 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:

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:

Finding the n^th term in the sequence

The following mathematical formula can be used to find the n^th triangular number in this sequence:

Other Number Sequences

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

• Finding the tirst 100 terms of different number sequences.
• Finding the n^th term of a number sequence.
• The Collatz Conjecture.

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:

• Calculating Pi using an infinite series.
• The legend of the chessboard.

Extra Challenge

You may also enjoy the following challenge:

• Calculating Euler’s Number.