# Arithmetic sequences

I can appreciate the features of an arithmetic sequence and be able to recognise one.

# Arithmetic sequences

I can appreciate the features of an arithmetic sequence and be able to recognise one.

## Lesson details

### Key learning points

- Finding the difference between each term can help you identify different types of sequence.
- Sequences with a constant difference are arithmetic sequences.
- Arithmetic sequences can be uniquely described with an initial term and a common difference.
- It is possible to identify which sequences are arithmetic.

### Common misconception

Sequences such as triangular numbers which have a linear sequence in their differences are linear.

Terms in an arithmetic sequence have to have a common first difference.

### Keywords

Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Video

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## Starter quiz

### 6 Questions

## Exit quiz

### 6 Questions

arithmetic sequence -

a sequence that increases or decreases by the same step

common difference -

the constant additive rule from one term to the next

initial term -

the first term in a sequence

successive terms -

terms that are next to each other in a sequence

7, 5, 3, 1, ... -

initial term $$7$$ and common difference $$-2$$

7, 9, 11, 13, ... -

initial term $$7$$ and common difference $$2$$

-1.6, -1.3, -1, -0.7, ... -

initial term $$-1.6$$ and common difference $$0.3$$

-1.6, -1.9, -2.2, -2.5, ... -

initial term $$-1.6$$ and common difference $$-0.3$$

-2, 3, 8, 13, ... -

fifth term $$18$$ and common difference $$5$$

38, 33, 28, 23, ... -

ninth term $$-2$$ and common difference $$-5$$