**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 :

a_{n} = a + (n - 1)d

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

**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

a_{2} = a + d

= 5 + (3/2)

= (10 + 3)/2

= 13/2

a_{3} = 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

a_{6} = 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

a_{2} = -2

Third term a₃ = a + 2 d

= -4 + 2(2)

= -4 + 4

a_{3} = 0

Fourth term = a + 3 d

= -4+3 (2)

= -4 + 6

a_{4} = 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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