# FIND THE MISSING TERM IN THE ARITHMETIC SEQUENCE

Find the Missing Term in the Arithmetic Sequence :

We find the the missing term using the formula for general term.

General term :

an  =  a + (n - 1)d

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

## Find the Missing Term in the Arithmetic Sequence - Examples

Question 1  :

Which term of the AP 3, 8, 13, 18,............ is 78?

Solution :

a = 3     d = t₂ -t = 8 - 3  ==>  5

an = 78

a + (n - 1) d = 78

3 + (n - 1) 5 = 78

(n - 1) 5 = 78 - 3

(n - 1) 5 = 75

n - 1 = 75/5

n - 1 = 15  ==>  n = 16

Hence 78 is 16th term of the given sequence.

Question 2 :

Find the number if terms in each of the following APs:

7, 13,19,.................205

Solution :

a = 7    d = t₂ -t₁  ==>  13 - 7  = 6

an = 205

a + (n -1) d = 205

7 + (n - 1) 6 = 205

(n - 1) 6 = 205 - 7

(n - 1) 6 = 198

n - 1 = 198/6

n - 1 = 33  ==>  n = 34

Therefore total number of terms is 34

Question 3 :

Find the number of terms of the given sequence

18, 15 ½ , 13,...............,-47

Solution :

a = 18    d = t₂ -t₁ 15  1/2 - 18

d  =  (31/2)  - 18

d  =  (31 - 36)/2  = -5/2

an = -47

a + (n -1) d = -47

18 + (n - 1) (-5/2) = -47

(n - 1) (-5/2) = -47 - 18

(n - 1) (-5/2) = -65

n - 1  =  (-65 x 2)/(-5)

n - 1  =  26

n  =  26 + 1  ==> n = 27

Hence total number of terms is 27.

Question 4 :

Check whether -150 is a term of the AP 11, 8, 5, 2,..........

Solution :

a = 11    d = t₂ -t₁= 8 - 11 = -3

an = -150

a + (n -1) d = -150

11 + (n - 1) (-3) = -150

(n - 1) (-3) = -150 - 11

(n - 1) (-3) = -161

n - 1 = (-161)/(-3)

n - 1  =  53.6

n = 53.6 + 1  ==>  n  =  54.6

So -150 is not one of term of the above sequence.

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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