HOW TO DETERMINE IF A SEQUENCE IS ARITHMETIC

Question 1 :

Check whether the following sequences are in A.P.

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

Solution :

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

(ii)  1/2, 1/3, 1/4, 1/5........

Solution :

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

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

Solution :

The given sequence is arithmetic progression.

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

Solution :

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

Solution :

The given sequence is not arithmetic progression.

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

Question 2 :

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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