arithmetic progression (Meaning)

Wordnet

arithmetic progression (n)

(mathematics) a progression in which a constant is added to each term in order to obtain the next term

Synonyms & Antonyms of arithmetic progression

No Synonyms and anytonyms found

arithmetic progression Sentence Examples

  1. An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which the difference between consecutive terms is constant.
  2. In an arithmetic progression, each term can be found by adding a fixed number, called the common difference, to the previous term.
  3. 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.
  4. Arithmetic progressions are extensively used in mathematics, physics, finance, and other fields to model linear growth or change.
  5. When plotting the terms of an arithmetic progression on a graph, the points form a straight line.
  6. The sum of the first \( n \) terms of an arithmetic progression can be calculated using the formula \( S_n = \frac{n}{2} \times (2a_1 + (n - 1) \times d) \).
  7. Arithmetic progressions play a crucial role in calculus, where they are used to understand the concept of limits and derivatives.
  8. 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.
  9. Studying the properties of arithmetic progressions helps develop problem-solving skills and mathematical reasoning.
  10. 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.