Arithmetic progression

In mathematics, an arithmetic progression, or arithmetic sequence, is a sequence. The difference between each two terms which follow one another is always the same. This is different from a geometric progression, where the ratio of change between two terms is constant.
If the initial term of an arithmetic progression is [math]\displaystyle{ a_1 }[/math] and the common difference is [math]\displaystyle{ d }[/math], then the [math]\displaystyle{ n }[/math]-th term of the sequence ([math]\displaystyle{ a_n }[/math]) is given by:

[math]\displaystyle{ 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 sum of a finite arithmetic progression is called an arithmetic series.

Arithmetic Progression Media

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  Proof without words of the arithmetic progression formulas using a rotated copy of the blocks.

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