arithmetic progression

Thân thiện

A student writes an arithmetic progression on the chalkboard.

Definition

1. Noun:
   • A sequence of numbers in which the difference between any two successive members is constant: An arithmetic progression is a mathematical sequence where each term after the first is found by adding a fixed, non-zero number, called the common difference, to the previous term.

Usage

• The term is used primarily in mathematics to describe a specific, linear pattern of numbers.
• It is often contrasted with other types of sequences, such as geometric progressions.
• It can be used to model situations involving constant, regular increase or decrease.

Examples

• Noun:
  • The sequence 2, 5, 8, 11, 14... is an arithmetic progression with a common difference of 3.
  • To find the 10th term of the arithmetic progression starting at 1 with a difference of 4, you use the formula.
  • The problem involved calculating the sum of the first 20 terms of a simple arithmetic progression.

Advanced Usage

• "In arithmetic progression": This phrase is used to state that a set of numbers follows this rule.
  • The ages of the three siblings were in arithmetic progression, with a difference of two years.
• The concept is foundational for understanding arithmetic series, which is the sum of the terms of an arithmetic progression.

Variants and Related Words

• Arithmetic sequence: A fully synonymous term for arithmetic progression.
• Common difference (n): The constant value (denoted as 'd') added to each term to get the next term in an arithmetic progression.
• Linear progression: A less technical term sometimes used to describe a similar pattern of constant change.

Synonyms

• Arithmetic sequence: (Mathematics) A sequence with a constant difference between consecutive terms.

Related Phrases and Concepts

• General term: The formula for the -th term of an arithmetic progression: , where is the first term and is the common difference.
• Sum of an arithmetic progression: The total of the first terms, given by the formula or .

Học thuật

Noun

1. (mathematics) a progression in which a constant is added to each term in order to obtain the next term
   • 1-4-7-10-13- is the start of an arithmetic progression