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Teaching mathematics
Teaching mathematics

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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.