Editing Arithmetic progression (section)

{{Short description|Sequence of equally spaced numbers}}
[[File:Arithmetic_progression.svg|thumb|[[Proof without words]] of the arithmetic progression formulas using a rotated copy of the blocks.]]
An '''arithmetic progression''' or '''arithmetic sequence''' is a [[sequence]] of [[number]]s 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 <math>a_1</math> and the common difference of successive members is <math>d</math>, then the <math>n</math>-th term of the sequence (<math>a_n</math>) is given by
:<math>a_n = a_1 + (n - 1)d.</math>
A finite portion of an arithmetic progression is called a '''finite arithmetic progression''' and sometimes just called an arithmetic progression. The [[summation|sum]] of a finite arithmetic progression is called an '''arithmetic series'''.