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An Arithmetic Sequence or Progression (abbreviated as A.P) is a sequence in which each term after the first is obtained by adding to the preceding term, a fixed number which is called the common difference.
In other words, quantities are said to be in Arithmetic Sequence, when they increase or decrease by a by common difference. Thus each of the following series forms an arithmetic progression.
The common difference is found by subtracting any term of the series from that which follows it. In the first of the above examples, the common difference is  ; in the second it is  ; in the third it is  .
But 
is not an A.P. Here the second term minus first term is  , while the third term minus the second is  , the difference so obtained does not remain the same.
The nth term of an Arithmetic Progression:
Let  be the first term and  be the constant difference. Then the second term is  , the third term is  . In each of these terms, the coefficient of  is  less than the number of term. Similarly, the 10th term is . The nth term is the  term after the first term and is obtained after has added  times in succession. Hence, if  represents the  term, then
Example:
Find the seventh term of an A.P in which the first term is  and the common difference is .
Solution:
The seventh term may be designed as , we use
as the formula and substitute for the variables to find ;
Here  ,  , 
 
Thus, the required seventh term is  .
Example:
Find the  term of the following arithmetic progression.
Solution:
Here  ,  , 
 
Gives 
Thus, the required  term is  .
Example:
Find the  term of an A.P. whose  term is  and the  term is  .
Solution:
Using  , we have
  ------- (1)
  ------- (2)
Subtracting (1) and (2), we get
 
Putting the value  in (1), we obtain
  
Putting  ,  ,  in  we get
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