1.  An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding
 a fixed number $d$ to the preceding term, except the first term. The fixed number $d$ is called the
 common difference.
The general form of an AP is $a,  a + d,  a + 2d,  a + 3d, . . . $

2.  A given  list  of  numbers  $a_1,a_2,a_3......a_n$ is  an AP,  
 if  the  differences  $a_2-a_1$ ,$a_3-a_2$,... give the same value, 
 i.e., if $a_{k+1}-a_k$ is the same for different values of k.

3.  In an AP with first term $a$ and common difference $d$, the nth term (or the general term) 
    is given by     $a_n = a + (n – 1) d.$ 
	
4.  The sum of the first n terms of an AP is given by :
     $S_n$=$n/2$$[2a+(n-1)d]$

5.  If $l$ is the last term of the finite AP, say the nth term, then the sum of all terms of the AP
is given by 
           $S$=$n/2$$[a+l]$
		   

6.. If  $a$,  $b$,  $c$  are  in AP,  then  $b={a+c}/2$ and $b$ is called mean  of  $a$  and  $c$.