We have already looked at sequences earlier in the year. Now we want to focus more carefully on how to find the nth term of different sequences. The nth term is a rule that let’s us calculate the value of a specific term of the sequence, given its position in the sequence (e.g. the 213th term in the sequence).

Linear sequences

A linear sequence (also known as an arithmetic sequence) is one where each term in the sequence is a fixed amount larger than the previous term. eg. 10, 13, 16, 19, 22, … is a linear sequence.

For this kind of sequence we can use a special technique to calculate the nth term of the sequence.

This technique is illustrated below:

Let’s try this together for a few sequences from the following:

Exercise

Now let’s try the textbook exercise 1 on pages 221 to 223 of the textbook. In this exercise some sequences are written in a column within a table. This does not change the mathematics that we will use at all:

The answers are below: