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Help on arithmetic sequence problem

  1. Feb 13, 2009 #1
    If the sum of the first 10 terms and the sum of the first 100 terms of a given arithmetic progression are 100 and 10, respectively, what is the sum of first 110 terms?

    S(10) = (10/2) (a1 + a10) = 100
    S(100) = (100/2) (a1 + a100) = 10

    a1 + a10 = 20
    a1 + a100 = 0.20

    a100 = a1 + 99d
    a10 = a1 + 9d

    i subtracted and got:
    a10 - a100 = 19.8
    a1 + 9d - a1 - 99d = 19.8
    d = -0.22

    S(110) = (110/2) (a1 + a110)
    a110 = a100 + 10d

    S(110) = 55 (a1 + a100 - 2.2) = 55(0.20 - 2.2) = 55(-2) = -110

    is this correct?
     
  2. jcsd
  3. Feb 14, 2009 #2
    Yes; well done!
     
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