arithmetic series - definição. O que é arithmetic series. Significado, conceito
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O que (quem) é arithmetic series - definição

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
  • Animated proof for the formula giving the sum of the first integers 1+2+...+n.

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, .
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.).
Arithmetic geometry         
  • The [[hyperelliptic curve]] defined by <math>y^2=x(x+1)(x-3)(x+2)(x-2)</math> has only finitely many [[rational point]]s (such as the points <math>(-2, 0)</math> and <math>(-1, 0)</math>) by [[Faltings's theorem]].
BRANCH OF ALGEBRAIC GEOMETRY FOCUSED ON PROBLEMS IN NUMBER THEORY
Arithmetical algebraic geometry; Arithmetic Geometry; Arithmetic algebraic geometry; Arithmetic Algebraic Geometry
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.

Wikipédia

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 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n}} ) is given by:

a n = a 1 + ( n 1 ) d {\displaystyle 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.