FIND THE MISSING TERM IN THE ARITHMETIC SEQUENCE

Question 1  :

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

Solution :

a = 3     d = t₂ -t₁ = 8 - 3  ==>  5  

a_n = 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 

a_n = 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 

a_n = -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

a_n = -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 the terms of the above sequence.

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