HOW TO FIND THE MISSING TERMS IN AN ARITHMETIC SEQUENCE

How to Find the Missing Terms in an Arithmetic Sequence ?

By using the formula for general term of an arithmetic sequence, we find the missing term.

General term :

an  =  a + (n - 1)d

a = first term, d = common difference and n = indicated term

How to Find the Missing Terms in an Arithmetic Sequence - Questions

Question 1 :

Find 30th term of the AP :

10, 7, 4,....... is

Solution :

a = 10  d = a₂ - a₁  ==>  7 - 10 = -3

an  =  a + (n - 1 ) d

=  10 + (30 - 1) (-3)

=  10 + 29 (-3)

=  10 - 87

=  -77

Hence the 4th term is -77.

Question 2 :

Find  11th term of the AP -3,-1/2,2,.......... is

(A) 28     (B) 22     (C) -38      (D) -48 ½

Solution :

a = -2  d = a₂ - a ₁               n = 11

d  =  -1/2 - (-3)

=  (-1/2) + 3

=  (-1 + 6)/2

=  5/2

an = a + (n - 1 ) d

=  -3 + (11 - 1) (5/2)

=  -3 + 10 (5/2)

=  -3 + 25

=  22

Hence the 11th term is 22.

Question 3 :

In the following AP s, find the missing term in the boxes

(i)  2,  ____ , 26

Solution :

a ₁ = 2        a₃ = 26

from this we need to find the value of a ₂

a₃ = 26

a + 2 d = 26

2 + 2 d = 26

2 d = 26 - 2

2 d = 24

d = 24/2,  d = 12

Second term :

a2  =  a + d

a2  = 2 + 12

a2 =  2 + 12

=  14

Hence the second term is 14.

(ii) ____, 13 , ___ , 3

Solution :

a2 = 13

a4 = 3

a + d = 13 --------(1)

a + 3 d = 3 --------(2)

(1) - (2)

a + d = 13

a + 3 d = 3

(-)   (-)  (-)

--------------

- 2 d = 10

d = 10/(-2)

d = -5

Substitute d = -5 in the first equation

a + d = 13

a - 5 = 13

a = 13 + 5

a = 18

First term = 18

Third term = a + 2 d = 18 + 2 (-5)

= 18 - 10

= 8

Third term = 8

After having gone through the stuff given above, we hope that the students would have understood, how to find the missing terms in an arithmetic sequence

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