Teaching mathematics
Teaching mathematics

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Teaching mathematics

2 Sequences as functions

A sequence is a collection of numbers or objects that are arranged in order. Each of these numbers or objects is called a ‘term’, so a sequence has a first term, second term, third term, etc.

Note that this is the same word, but not the same meaning, as the ‘terms’ that you find in an expression. You do not rearrange, add or subtract the terms of a sequence. It is wise to avoid using the word in different ways within one lesson.

All of the sequences you meet in school mathematics have a rule.

Activity 3 Sequences and rules

Timing: Allow 5 minutes

What is the next term in each sequence in Figure 6?

What is the rule for each sequence? Write it in words, and as an algebraic expression if you can.

Figure 6 Sequences

Keep a note of your work on this activity as you will use it in the next section.


For the first five sequences the sixth terms are 30, 96, 1/36 and S. The last sequence is a diagram with six triangles.


Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371