Explanation:
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 a_{1} 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.
Sum
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:
An alternate form results from re-inserting the substitution: a_{n} = a_{1} + (n − 1) d:
(Our solved example in mathguru.com uses this concept).
http://en.wikipedia.org/wiki/Arithmetic_progression
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