**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 :

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

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

**Question 1 :**

Find 30th term of the AP :

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

**Solution :**

a = 10 d = a₂ - a₁ ==> 7 - 10 = -3

a_{n} = 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

a_{n} = 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 :**

a_{2} = a + d

a_{2} = 2 + 12

a_{2} = 2 + 12

= 14

Hence the second term is 14.

(ii) ____, 13 , ___ , 3

**Solution :**

a_{2} = 13

a_{4} = 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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