How to find the next term in a linear sequence

Part ofMathsSequences

  • A linear sequence goes from one term to the next by always adding (or subtracting) the same value.

  • The number added (or subtracted) at each stage of the linear sequence is called the common difference.

  • Examples of linear sequences occur when things change by the same amount each time.

How to find the next term in a linear sequence

Have a go yourself

Skip image gallery
  1. A whiteboard, a whiteboard rubber and black and blue marker pens. Overlaid is a graphic reading: Step-by-step.

    Click to see a step-by-step slideshow.

How do they work?

Example 1

Here is the linear sequence:

8, 11, 14, 17…

  • To find the next term in this sequence we calculate the common difference.
  • In this example the common difference is +3.

8 (+3) 11 (+3) 14 (+3) 17 (+3) …

Therefore, the next term in the sequence would be 20 (17 + 3)

Example 2

Here is another linear sequence:

70, 60, 50, 40 …

In this example the common difference is -10, because 10 is subtracted from each term to give the next term in the sequence.

70 (-10) 60 (-10) 50 (-10) 40 (-10) …

The next term in the sequence will be 30 (40 – 10)

When a linear sequence is plotted on a graph, it always gives a straight line.

Five vertical lines of squares, increasing in height from left to right (one square, two squares, three squares, four squares, five squares). Arrows are drawn underneath, between each column and one next to it on the right. Below each of those arrows is written +1.
Shape pattern showing an arithmetic sequence. The common difference = +1

Common examples of linear sequences

  • Shape patterns (see image).
  • Someone walking the same distance every 10 minutes.
Five vertical lines of squares, increasing in height from left to right (one square, two squares, three squares, four squares, five squares). Arrows are drawn underneath, between each column and one next to it on the right. Below each of those arrows is written +1.
Shape pattern showing an arithmetic sequence. The common difference = +1

Linear sequence activity

Find out how much you know in this quick activity.

Arithmetic sequence quiz

Test your knowledge with this quick quiz.

Where next?

Discover more about this topic from Bitesize.

Algebra

More on Sequences

Find out more by working through a topic