arithmetic progression: meaning, definition, pronunciation and examples
C2/AcademicTechnical/Academic
Quick answer
What does “arithmetic progression” mean?
A sequence of numbers in which the difference between consecutive terms is constant.
Audio
Pronunciation
Definition
Meaning and Definition
A sequence of numbers in which the difference between consecutive terms is constant.
A foundational concept in mathematics describing linear growth, used as a model in various real-world applications involving consistent additive change.
Dialectal Variation
British vs American Usage
Differences
No significant differences in usage or definition. Spelling follows regional conventions: 'Maths' (UK) vs. 'Math' (US) in surrounding text.
Connotations
Neutral technical term in both varieties.
Frequency
Common with equal frequency in secondary and tertiary mathematics education contexts in both regions.
Grammar
How to Use “arithmetic progression” in a Sentence
[The sequence] is an arithmetic progression[X] forms an arithmetic progressionThe arithmetic progression with first term [a] and common difference [d]Vocabulary
Collocations
Examples
Examples of “arithmetic progression” in a Sentence
adjective
British English
- The growth followed an arithmetic-progression model.
- He derived an arithmetic-progression formula.
American English
- The data showed an arithmetic-progression pattern.
- She used an arithmetic-progression approach.
Usage
Meaning in Context
Business
Rare; might appear in forecasting or depreciation calculations (e.g., 'The asset depreciated in an arithmetic progression').
Academic
Core term in mathematics curricula, foundational for algebra and number theory.
Everyday
Rare, except in specific educational or problem-solving contexts.
Technical
Standard term in pure and applied mathematics, computer science (algorithm analysis), and physics.
Vocabulary
Synonyms of “arithmetic progression”
Neutral
Weak
Vocabulary
Antonyms of “arithmetic progression”
Watch out
Common Mistakes When Using “arithmetic progression”
- Misspelling as 'arithmatic progression'.
- Confusing 'common difference' with 'common ratio' (which belongs to geometric progression).
- Using the term for any increasing sequence, not only those with a constant difference.
FAQ
Frequently Asked Questions
They are closely related. An arithmetic progression is a discrete sequence, while a linear function describes a continuous line. The points of an arithmetic progression lie on a linear function.
Yes. A negative common difference results in a decreasing sequence, like 10, 7, 4, 1, ... which is still a valid arithmetic progression.
The nth term is given by a_n = a_1 + (n-1)*d, where a_1 is the first term and d is the common difference.
It models scenarios with regular additive change, such as weekly savings plans, constant speed motion over equal time intervals, or seating arranged in rows with a fixed number of extra seats per row.
A sequence of numbers in which the difference between consecutive terms is constant.
Arithmetic progression is usually technical/academic in register.
Arithmetic progression: in British English it is pronounced /əˌrɪθ.mə.tɪk prəˈɡreʃ.ən/, and in American English it is pronounced /əˌrɪθ.mə.t̬ɪk prəˈɡreʃ.ən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Arithmetic Progression Adds the same amount Repeatedly. Think 'APA' - Add, Progression, Amount.
Conceptual Metaphor
CONSISTENT STEPS (e.g., climbing stairs where each step is the same height).
Practice
Quiz
Which of the following is the defining characteristic of an arithmetic progression?