Mathguru – Help – In an arithmetic progression, find the nth term from the end.

Solved Example > No. SE 12

In an arithmetic progression, find the nth term from the end.

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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 a₁ and the common difference of successive members is d, then the nth term of the sequence is given by:

$\ a_n = a_1 + (n - 1)d,$

and in general

$\ a_n = a_m + (n - m)d.$

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

http://en.wikipedia.org/wiki/Arithmetic_progression

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.

(Our solved example in mathguru.com uses the below concept. This is our own explanation, it is not taken from Wikipedia.)

N^th term from the end is given by the formula

N^th term from the end = {l - (n-1) d}

l is the last term of the AP

n is the number of terms

d is the common difference