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.
These resources will be removed by end of Summer Term 2025.
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.
Keywords
Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.
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.
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).
Lesson 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 $$-5$$
