When the sequence of numbers (or a_{1}, a_{2}, a_{3},...) increases or decreases by a fixed quantity, then the sequence is in arithmetic progression (A.P.). The fixed quantity is called as *common difference*. For an AP, we define its first term as *a* and the common difference as *d*.
The general expression for an AP is: *a*, *a* + *d*, *a* + 2*d*, *a* + 3*d*,....

If T_{r} represents the gernal term of an AP, then
where

In an AP, the difference of any two consecutive terms is *d* and is given by:

## Sum of *n* terms of an AP

Consider *n* terms of an AP with first term as a and common difference as d. Let S_{n} denote the sum of first *n* terms, then

where

## Arithematic Mean

To understand the topic better, go to *Arithmetic mean*.
When three quantities are in AP, then the middle one is called as arithmetic mean of other two. If *a* and *b* are two numbers and A be the arithmetic mean of *a* and *b*, then *a*, A, *b* are in AP.

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