Arithmetic Progression

Introduction:

        It is a sequence of numbers in which each term except the first term can be calculated by adding constant number (common difference) to the immediately preceding number. Quantities are said to be in Arithmetic progression when they increase or decrease by a common difference.

The General form of the arithmetic sequence is,
     a, a+d, a+2d, a+3d………..
Here a is the first number and d is the common difference.
To find the nth term of an arithmetic progression we can use the following formula,
     a_n=a+ (n-1) d
Properties of Arithmetic Progression:

• When we add or subtract any constant number with all the terms of the sequence, the arithmetic sequence remains an arithmetic sequence.

     Example:
     5, 7, 9, 11, 13, 15, 17….. is an A.P with common difference 2.
     Add 3 with all the terms,
     8, 10, 12, 14, 16, 18, 20…. Is also an A.P with common difference 2.

• When we multiply or divide by a non-zero constant with all the terms of the sequence, the arithmetic progression sequence remains an arithmetic progression.

Hope you liked the above explanation. Please leave your comments, if you have any doubts.