# Sequences & Series resources

### Quick Reference (1)

Arithmetic and geometric progressions

Arithmetic and geometric progressions are particular types of sequences of numbers which occur frequently in business calculations. This leaflet explains these terms, and shows how the sums of these sequences can be found.

### Teach Yourself (3)

Limits of sequences

In this unit, we recall what is meant by a simple sequence, and introduce
infinite sequences. We explain what it means for two sequences to be the same,
and what is meant by the n-th term of a sequence. We also investigate the
behaviour of infinite sequences, and see that they might tend to plus or minus
infinity, or to a real limit, or behave in some other way.

Sigma notation

Sigma notation is a method used to write out a long sum in a concise way. In
this unit we look at ways of using sigma notation, and establish some useful
rules.

The sum of an infinite series

In this unit we see how finite and infinite series are obtained from finite and
infinite sequences. We explain how the partial sums of an infinite series form
a new sequence, and that the limit of this new sequence (if it exists) defines
the sum of the series. We also consider two specific examples of infinite
series that sum to e and pi respectively.

### Video (1)

Arithmetic and Geometric Progressions

This unit introduces sequences and series, and gives some simple examples
of each. It also explores particular types of sequence known as arithmetic
progressions (APs) and geometric progressions (GPs), and the corresponding series. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.