When the sequence of numbers (or a1, a2, a3,...) 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 + 2d, a + 3d,....
If Tr 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 Sn denote the sum of first n terms, then
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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