How to find the next term in an arithmetic sequence

  • An arithmetic 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 arithmetic sequence is called the common difference.

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

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How do they work?

Example 1

Here is an arithmetic 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 arithmetic 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 an arithmetic sequence is plotted on a graph, it always gives a straight line.

Common examples of arithmetic sequences

  • Shape patterns (see image).
  • Someone walking the same distance every 10 minutes.
Shape pattern showing an arithmetic sequence. The common difference = +1

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