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?
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)
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.
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