Arithmetic Series Worksheet Solution2





In the page arithmetic series worksheet solution2 you are going to see solution of each questions from the arithmetic series worksheet.

(ii) 6 + 5 ¼ + 4 ½ + ......... 25 terms

Solution:

In this series we have 25 terms so n = 25

 a = 6      d = t₂ - t₁

                = 5 ¼ - 6

                = (21/4)  - 6

                = (21-24)/4

             d = -3/4

    Sn = (n/2) [ 2a + (n-1) d ]

    S₂₅ = (25/2) [ 2(6) + (25-1) (-3/4) ]

         = (25/2) [ 12 + (24) (-3/4) ]

         = (25/2) [ 12 + (6) (-3) ]

         = (25/2) [ 12 - 18 ]

         = (25/2) [ -6 ]

         = (25) [ -3 ]

        = -75


(4) Find the sum of each arithmetic series described

(i) a = 5 n = 30 and L = 121

Solution:


       S n = (n/2) [ a+ L ]

            = (30/2) [ 5 + 121 ]

            = (15) [126]

        S₃₀ = 1890 


(ii) a = 50    n = 25    and d = -4

Solution:


       S n = (n/2) [ 2a + (n-1) d ]

       S₂₅ = (25/2) [ 2(50) + (25-1) (-4) ]

            = (25/2) [ 100 + (24) (-4) ]

            = (25/2) [ 100 - 96 ]

            = (25/2) [4]

            = (25) [2]

           = 50 


(5) Find the sum of first 40 terms of the series

1² - 2² + 3² - 4²  + ........ 

Solution:


        =  1² - 2² + 3² - 4²  + ........ 40 terms

          = (1 - 4) + (9 - 16)  + ........ 20 terms

          = - 3 - 7 + ........ 20 terms

here a = -3   d = -7 - (-3)   n = 20

                      = -7 + 3 

                     d = -4 

       S n = (n/2) [ 2a + (n-1) d ]

            = (20/2) [ 2(-3) + (20-1) (-4)]

            = 10 [ -6 + 19 (-4)]

            = 10 [ -6 + 19 (-4)]

            = 10 [ -6 -76]

            = 10 [ -82]

            = -820


(6) In an arithmetic series,the sum of first 11 terms is 44 and the that of the next 11 terms is 55. Find the arithmetic series.

Solution:

Sum of first 11 terms = 44

                         S₁₁ = 44

     (11/2)[2a + (11-1) d] = 44

              2a + 10 d = (44 x 2)/11

              2a + 10 d = 4 x 2

              2 a + 10 d = 8   ----- (1)

Sum of next 11 term = 55

                S₂₂ = S₁₁ + 55

                S₂₂ = 44 + 55

                S₂₂ = 99

     (22/2)[2a + (22-1) d] = 99

              2a + 21 d = (99 x 2)/22

              2a + 21 d = 9

              2 a + 21 d = 9   ----- (2)

Solving (1) and (2) we get

                      -11 d = -1

                            d = 1/11

Substitute d = 1/11 in the first  equation we get

          2 a + 10 (1/11) = 8

          2 a + 10/11 = 8

                    2 a  = 8 - (10/11)

                    2 a  = (88 - 10)/11

                    2 a  = 78/11

                      a  = 78/(2x11)

                      a = 39/11

Therefore the series is (39/11) + (40/11) + (41/11) + ............



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arithmetic series worksheet solution2