arithmetic progression Synonyms
No Synonyms and anytonyms found
arithmetic progression Meaning
arithmetic progression (n)
(mathematics) a progression in which a constant is added to each term in order to obtain the next term
arithmetic progression Sentence Examples
- An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which the difference between consecutive terms is constant.
- In an arithmetic progression, each term can be found by adding a fixed number, called the common difference, to the previous term.
- The formula to find the nth term of an arithmetic progression is given by \( a_n = a_1 + (n - 1) \times d \), where \( a_n \) is the nth term, \( a_1 \) is the first term, and \( d \) is the common difference.
- Arithmetic progressions are extensively used in mathematics, physics, finance, and other fields to model linear growth or change.
- When plotting the terms of an arithmetic progression on a graph, the points form a straight line.
- The sum of the first \( n \) terms of an arithmetic progression can be calculated using the formula \( S_n = \frac{n}{2} \times (2a_1 + (n - 1) \times d) \).
- Arithmetic progressions play a crucial role in calculus, where they are used to understand the concept of limits and derivatives.
- In real-life scenarios, arithmetic progressions can represent situations like the steady increase in population over time or the depreciation of assets at a constant rate.
- Studying the properties of arithmetic progressions helps develop problem-solving skills and mathematical reasoning.
- Understanding arithmetic progressions is fundamental for grasping more advanced topics in algebra and number theory.
FAQs About the word arithmetic progression
(mathematics) a progression in which a constant is added to each term in order to obtain the next term
No synonyms found.
No antonyms found.
An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which the difference between consecutive terms is constant.
In an arithmetic progression, each term can be found by adding a fixed number, called the common difference, to the previous term.
The formula to find the nth term of an arithmetic progression is given by \( a_n = a_1 + (n - 1) \times d \), where \( a_n \) is the nth term, \( a_1 \) is the first term, and \( d \) is the common difference.
Arithmetic progressions are extensively used in mathematics, physics, finance, and other fields to model linear growth or change.
