Arithmetic and geometric progressions

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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.
In order to master the techniques explained here it is vital that you undertake plenty of practice
exercises so that they become second nature.
After reading this text, and/or viewing the video tutorial on this topic, you should be able to:
• recognise the difference between a sequence and a series;
• recognise an arithmetic progression;
• find the n-th term of an arithmetic progression;
• find the sum of an arithmetic series;
• recognise a geometric progression;
• find the n-th term of a geometric progression;
• find the sum of a geometric series;
• find the sum to infinity of a geometric series with common ratio |r| < 1.
Contents
1. Sequences 2
2. Series 3
3. Arithmetic progressions 4
4. The sum of an arithmetic series 5
5. Geometric progressions 8
6. The sum of a geometric series 9
7. Convergence of geometric series 12
Download Arithmetic and geometric progressions PDF file.