PROPERTIES OF ARITHMETIC PROGRESSIONS

1. If each term of an A.P are added or subtracted with the same constant, then the resulting sequence is also in A.P with the same common difference.

Example:

2, 5, 8, 11, 14, …………………….. . are in A.P.

d = 3

when k = 2 is added in each term

4, 7, 10, 13, 16, ……………………………… .are in A.P.

d = 3

when k = 3 is subtracted in each term

1, 4, 7, 10, 13, ……………………….. . are in A.P.

2. If each term of an A.P are multiplied or divided with the same constant, then the resulting sequence is also in A.P. and common difference also multiplied or divided with the same constant.

Example:

2, 5, 8, 11, 14, …………………….. . are in A.P.

d = 3

when k = 4 is multiplied in each term

8, 20, 32, 44, 56, …………………… .are in A.P.

d = 12 = 3 x 4.

3. The sum of two terms equidistant from the beginning and from the end is equal to the sum of first and the last term of an A.P.

Example:

2, 6, 10, 14, 18, 22, 26 are in A.P

Here n = 7

First term from beginning and end t1 + t7 = 2+ 26 = 28

Second term from beginning and end t2 + t6 = 6 + 22 = 28

Third term from beginning and end t3 + t5 = 10 + 18 = 28

Fourth term from beginning and end t4 + t4 = 14 + 14 =28

Post Author: E-Maths