Meaning & use
arithmetic sequence
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Meanings
phrasecountablemathematics
A list of numbers in order in which every number is found by adding the same fixed amount to the one before it.
Grammar: A noun phrase: an arithmetic sequence.
Patterns
- an arithmetic sequence with a common difference of 3
- the nth term of an arithmetic sequence
The numbers 4, 7, 10, 13 form an arithmetic sequence.
In an arithmetic sequence with first term 5 and difference 2, the fourth term is 11.
Students found the formula for the nth term of an arithmetic sequence.
phrasecountable
Any pattern in real life or a model where a quantity rises or falls by an equal step each time.
Grammar: Used when applying the idea to real situations, such as savings that grow by the same amount each month.
Patterns
- follow an arithmetic sequence
Her weekly savings of $10 more each week form an arithmetic sequence.
Seat numbers along one side of a row often follow an arithmetic sequence.
The rungs on the ladder are spaced so their heights form an arithmetic sequence.
Word forms
| plural | arithmetic sequences |
|---|
Common combinations
- common difference
- The common difference of this arithmetic sequence is negative four.
- nth term of an arithmetic sequence
- We wrote a rule for the nth term of an arithmetic sequence.
- sum of an arithmetic sequence
- Gauss found a quick way to compute the sum of an arithmetic sequence.
- first term of the sequence
- The first term of the sequence is 8.
- form an arithmetic sequence
- The odd numbers form an arithmetic sequence.
Synonyms and how they differ
- arithmetic progression
- Arithmetic progression means the same thing and is the more traditional term in many textbooks.
- linear sequence
- Linear sequence is the term often used in school curricula, referring to a pattern that graphs as a straight line.
Opposites
Word family
- arithmetic series noun
- the sum of the terms of an arithmetic sequence
- geometric sequence noun
- a sequence formed by multiplying by a fixed ratio
- term noun
- one number in a sequence
Commonly confused: arithmetic sequence or arithmetic series?
arithmetic sequence vs arithmetic series
A sequence is the ordered list of numbers, while a series is what you get when you add those numbers together.
Practice
Which list is an arithmetic sequence?
Choose one answer.
3, 8, 13, 18 increases by 5 each time. 2, 6, 18, 54 multiplies by 3, 1, 4, 9, 16 are squares, and 5, 6, 8, 11 has differences that keep changing.
Make it your own
Write a sentence using “arithmetic sequence”, then check it and compare it with the examples above.