# HOW TO CHECK IF THE GIVEN SEQUENCE IS ARITHMETIC SEQUENCE

How to Check If the Given Sequence is Arithmetic Sequence :

Here we are going to see how to check whether the given sequence is arithmetic sequence or not.

## How to Check If the Given Sequence is Arithmetic Sequence ?

The difference between any two consecutive terms of an A.P. is always constant. That constant value is called the common difference.

If the common difference are same, then the given sequence is A.P

Question 1 :

Check whether the following sequences are in A.P.

(i) a - 3, a - 5, a -7,...

Solution :

 d = t2 - t1d = (a - 5) - (a - 3)  =  a - 5 - a + 3d  =  -2 d = t3 - t2d = (a - 7) - (a - 5)  =  a - 7 - a + 5d  =  -2

Since the common difference area same, the given sequence is arithmetic progression.

(ii)  1/2, 1/3, 1/4, 1/5........

Solution :

 d = t2 - t1d = (1/3) - (1/2)  =  (2 - 3)/6d  =  -1/6 d = t3 - t2d = (1/4) - (1/3)  =  (3 - 4)/12d  =  -1/12

The common differences are not equal. Hence the given sequence is not A.P.

(iii) 9, 13, 17, 21, 25,...

Solution :

 d = t2 - t1d = 13 - 9d  =  4 d = t3 - t2d = 17 - 13d  =  4

The given sequence is arithmetic progression.

(iv) -1/3, 0, 1/3, 2/3.........

Solution :

 d = t2 - t1d = 0 - (-1/3)d  =  1/3 d = t3 - t2d = (1/3) - 0d  =  1/3

(v) 1, -1, 1, -1, 1, -1,............

Solution :

 d = t2 - t1d = -1 - 1d  =  -2 d = t3 - t2d = 1 - (-1)=  1 + 1  =  2

The given sequence is not arithmetic progression.

## How to Find Arithmetic Progression with 1st Term and Common Difference

Question 1 :

First term a and common difference d are given below. Find the corresponding A.P.

(i) a = 5 , d = 6

Solution :

General form of A.P

a, a + d, a + 2d,...........

5, (5+6), (5, + 2(6)), ......................

5, 11, 17, ...................

(ii) a = 7 , d =−5

Solution :

a, a + d, a + 2d,...........

a = 7

a + d  =  7 + (-5)  =  2

a + 2d  =  7 + 2(-5)  =  7 - 10  =  -3

The required sequence is 7, 2, -3, .................

(iii) a = 3/4, d = 1/2

Solution :

a = 3/4

a + d  =  (3/4) + (1/2)  =  (3+2)/4  =  5/4

a + d  =  (3/4) + 2(1/2)  =  (3/4) + 1  =  7/4

Hence the required sequence is 3/4, 5/4, 7/4,...............

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