Meaning & use
an arithmetic sequence
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Meaning
nouncountablemathematics
A list of numbers where you add the same amount each time to get the next number.
Grammar: Countable: you can say 'an arithmetic sequence' or 'arithmetic sequences'. Often followed by 'with' and the common difference.
Patterns
- arithmetic sequence with a common difference
- the terms of an arithmetic sequence
2, 5, 8, 11 is an arithmetic sequence because you add 3 each time.
The teacher asked us to find the next term in the arithmetic sequence.
In an arithmetic sequence, the difference between consecutive terms is constant.
Word forms
| plural | arithmetic sequences |
|---|
Common combinations
- common difference of an arithmetic sequence
- The common difference of the arithmetic sequence 4, 7, 10 is 3.
- terms of an arithmetic sequence
- We learned how to find the sum of the terms of an arithmetic sequence.
- arithmetic sequence formula
- The arithmetic sequence formula helps you find any term without listing all of them.
Synonyms and how they differ
- arithmetic progression
- Arithmetic progression is the more formal term used in some textbooks; arithmetic sequence is more common in school math.
Word family
- arithmetic noun
- The branch of mathematics dealing with numbers and basic operations.
- arithmetic adjective
- Relating to arithmetic or to adding the same number repeatedly.
Commonly confused: an arithmetic sequence or geometric sequence?
an arithmetic sequence vs geometric sequence
In a geometric sequence you multiply by the same number each time, while in an arithmetic sequence you add the same number.
Practice
Which of these is an arithmetic sequence?
Choose one answer.
1, 3, 5, 7, 9 is arithmetic because you add 2 each time. Option 0 is geometric (multiply by 2), option 2 is the Fibonacci sequence, and option 3 is squares.
Make it your own
Write a sentence using “an arithmetic sequence”, then check it and compare it with the examples above.