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Example: Finding Common Difference for given Arithmetic Progression

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In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13, ... is an arithmetic progression with common difference 2.


If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:

and in general

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



The sum of the members of a finite arithmetic progression is called an arithmetic series.

Expressing the arithmetic series in two different ways:

Adding both sides of the two equations, all terms involving d cancel:

Dividing both sides by 2 produces a common form of the equation:

(Our solved example in mathguru.com uses this concept)


An alternate form results from re-inserting the substitution: an = a1 + (n − 1) d:





The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.