# 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.

## 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.

## Arithmetic sequence activity

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