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:

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

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:

n

^{th 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:

- 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**:

#### Extra Challenge

You may also enjoy the following challenge: