# FINDING THE MISSING TERMS IN AN ARITHMETIC SEQUENCE

Finding 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

## Finding the Missing Terms in an Arithmetic Sequence - Examples

Question 1 :

Find the second and third of the given sequence

5, ____ , _____ , 9   1/2

Solution :

a = 5     a₄ = 9  1/2  =  19/2

a + 3 d  =  19/2

5 + 3 d  =  17/2

3 d  =  (19/2) - 5

3 d  =  (19 - 10)/2

3 d = 9/2

d  =  9/(2 x 3)  ==> d = 3/2

a2  =  a + d

=  5 + (3/2)

=  (10 + 3)/2

=  13/2

a3 = a + 2 d

=  5 + 2(3/2)

=  5 + 3

=  8

Hence the second and third terms are 13/2 and 8.

Questions 2 :

Find the missing terms of the sequence

-4,____,____,___,_____,6

Solution :

a = -4

a6 = 6

a + 5 d = 6

-4 + 5 d = 6

5 d = 6 + 4

5 d = 10

d = 10/5  => d  =  2

Second term  =  a₂  =  a + d

=  -4 + 2

a2  =  -2

Third term a₃ = a + 2 d

=  -4 + 2(2)

= -4 + 4

a3 = 0

Fourth term = a + 3 d

=  -4+3 (2)

=  -4 + 6

a4  =  2

Fifth term = a + 4 d

=  -2 + 4 (2)

=  -2 + 8

= 6

Question 3 :

Find the missing terms of the given sequence

______,38 , ______ , ______ , ____ , -22

Solution :

a ₂ = 38

a₆ = -22

a + d = 38 --------(1)

a + 5 d = -22 --------(2)

(2) - (1)

a + 5 d = -22

a +  d = 38

(-)   (-)  (-)

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

4 d = -60

d = -60/4

d = -15

Substitute d = -15 in the first equation

a + d = 38

a - 15 = 38

a = 38 + 15

a = 53

First term = 53

a ₃ = a + 2d = 53 + 2 (-15) = 23

a ₄ = a + 3d = 53 + 3 (-15) = 8

a ₅ = a + 4d = 53 + 4 (-15) = -7

Hence first, third, fourth and fifth terms are 53, 23, 8 and -7 respectively.

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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