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What (who) is arithmetical progression - definition

SEQUENCE OF NUMBERS WITH CONSTANT DIFFERENCES BETWEEN CONSECUTIVE NUMBERS

Arithmetic series; Arithmetic Progression; Arithmetic sequence; Arithmetic progressions; Arithmetical progression; Land-1; Arithmatic series; Arithmatic progression; Arithmetic Series; Arithmetic sum; Infinite arithmetic series; Infinite arithmetic sequence; Progression (arithmetic series); Common difference; Linear sequence

Arithmetic progression

An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, .

https://en.wikipedia.org/wiki/Arithmetic_progression

arithmetic progression

(also arithmetic series)

¦ noun a sequence of numbers in which each differs from the preceding one by a constant quantity (e.g. 1, 2, 3, 4, etc.; 9, 7, 5, 3, etc.).

Generalized arithmetic progression

A SET OF INTEGERS CONSTRUCTED AS AN ARITHMETIC PROGRESSION

Multiple arithmetic progression; Generalised arithmetic progression; Linear set; Semilinear set; Linear Set; Semilinear Set; Multidimensional arithmetic progression; Multi-dimensional arithmetic progression

In mathematics, a generalized arithmetic progression (or multiple arithmetic progression) is a generalization of an arithmetic progression equipped with multiple common differences – whereas an arithmetic progression is generated by a single common difference, a generalized arithmetic progression can be generated by multiple common differences. For example, the sequence 17, 20, 22, 23, 25, 26, 27, 28, 29, \dots is not an arithmetic progression, but is instead generated by starting with 17 and adding either 3 or 5, thus allowing multiple common differences to generate it.

https://en.wikipedia.org/wiki/Generalized_arithmetic_progression

Wikipedia

Arithmetic progression

An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2.

If the initial term of an arithmetic progression is $a_{1}$ and the common difference of successive members is $d$ , then the $n$ -th term of the sequence ( $a_{n}$ ) is given by:

a_{n}=a_{1}+(n-1)d

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

https://en.wikipedia.org/wiki/Arithmetic progression

Examples of use of arithmetical progression

1. G. Wells calls ‘the urgency of sex‘, and that Mrs S. was no isolated phenomenon, but merely the current figure in an arithmetical progression that had been robustly maintained for nearly 20 years.