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Arithmetic Progression is a sequence of such numbers whose difference of two consecutive terms is constant. Constant quantity is known as common difference. It is represented by letter ‘d’.
 
For example: Following sequences are n arithmetic progression.
1, 2, 3, 4, …. (common difference = -1)
8, 5, 2, -1, -4, ... (common difference = -3)
a, a - d, a - 2d, a - 3d, …. (common difference = -d)
If first term of an arithmetic progression is a and common difference is d, then:
nth term of arithmetic progression = a + (n – 1)d
Sum of first n terms Sn =
1
2
 n (a + l) [l = last term]  
Sum of n terms of arithmetic progression =
1
2
 n [2a + (n -1)d]
Arithmetic mean of two terns a and b
  A =
a + b
2
 
If nth term of series is a linear expression, then that series will be arithmetic progression.
If sum of n terms of any series is quadratic expression, then that series will be arithmetic progression.
If same quantity is added or subtracted from each term of an arithmetic progression, then new series formed will also be an arithmetic progression.
If same quantity is multiplied or divided by each term of an arithmetic progression then new series formed will also be an arithmetic series.
If corresponding terms of two series are added or subtracted then new series formed will be also an arithmetic series.
Series formed by multiplying or dividing corresponding terms of two arithmetic progression, then series formed will be not an arithmetic series.
 
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