In mathematics, an Arithmetic Progression or arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an arithmetic progression with common difference 2.We usually come across many problems related to arithmetic progression,and we can solve these problems once we learn to identify the sequences.These are basically a set of numbers arranged in a definite order according to some definite rule is called a sequence.A sequence is a function whose domain is the set N of natural numbers.
Indicated sum of the terms in a sequence is called a series.The result of performing the additions is the sum of the series.It is easy to identify the sequence in arithmetic progression as soon as we look at the problem,let us now look at the examples of arithmetic progression.
Quantities are said to be in Arithmetic progression when they increase or decrease by a common difference.
Examples:
Each one of the following series form an Arithmetic progression
i) 1, 3, 5, 7, …
ii) 3, 7, 11, 15, …
iii) 15, 12, 9, …
iv) x, x - d, x - 2d, .....
The common difference is found by subtracting any term of the series from the immediate succeeding term.
In the above example, common difference in the first is 2, in the second it is 4, in the third it is -3, in the fourth it is -d and in the fifth it is d.
The general form of an A.P. is as follows:
a = first term, d = common difference, then A.P. is a, a+d, a+2d, a+3d,.....
Hope you like the above example of Arithmetic progression.
Please leave your comments, if you have any doubts.
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