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Arithmetic Progression Problem

  1. Mar 17, 2014 #1
    1. The problem statement, all variables and given/known data
    If the sum of the first 7 terms of an arithmetic progression is 28 and the sum of the first 15 terms is 90, find the sum of n terms.:eek:


    2. Relevant equations
    Sn = 0.5n[2a+(n-1)d]
    a is the first term and d is the common difference. n is the number of terms.
    nth term = a + (n-1)d


    3. The attempt at a solution
    (here goes :uhh:)
    (1)..........a + 6d = 28
    (2)..........a + 14d = 90
    (2)-(1).....8d = 62
    ...............d = 7.75 (ok :cool:)
    (1)..........a + 6(7.75) = 28
    ..............a = -18.5 (yea! :biggrin:)
    (drumrollllllllllll)
    Sn = 0.5n(-37 + (n-1)7.75)
    = -18.5n +n(n-1)3.875
    = n[3.875(n-1) - 18.5] :approve:
    ...:mad: now what? the answer was n/4(n + 9)
     
  2. jcsd
  3. Mar 17, 2014 #2
    You have used formula of the nth term instead of using that of sum of n terms .28 is not the 7th term .Instead it is the sum of first 7 terms .Similarly with 90 being the sum of first 15 terms.

    Use Sn = (n/2)[2a+(n-1)d]
     
    Last edited: Mar 17, 2014
  4. Mar 18, 2014 #3
    ahh! I forgot! thanks
     
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