10th CBSE math solution for exercise 5.2 part 4

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10th CBSE math solution for exercise 5.2 part 4

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

Solution:

a = 3     d = t₂ -t₁       a n = 78

               = 8 - 3

               = 5 

   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 = 15 + 1

                   n = 16

Therefore 78 is 16th term of the given sequence


(5) Find the number if terms in each of the following APs:

(i) 7, 13,19,.................205

Solution:

a = 7    d = t₂ -t₁       a n = 205

               = 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 = 33 + 1

             n = 34

Therefore total number of terms is 34


(ii) 18, 15 ½ , 13,...............,-47

Solution:

a = 18    d = t₂ -t₁       a n = -47

               = 15 ½ - 18

               = (31/2)  - 18

               = (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

Therefore total number of terms is 27.


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

Solution:

a = 11    d = t₂ -t₁       a n = -150

               =  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 term of the above sequence.




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