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IB Math Methods questions

  1. Sep 9, 2003 #1
    I've been working on these problems for a long time trying to prove to myself that I'm not stupid (though I am convinced I am because I don't feel like "IB material" at the moment), but this will be impossible since I have other things to do. So, my two questions are these:

    1. An arithmetic sequence has a common difference of 2 and a sum of 120. The first term is numerically equal to the number of terms. FInd all possible values of hte first.

    I know that the answer is 8 because it is a multiple choice question and through elimination, the others aren't possible, but I don't understand how to prove this mathematically.

    2. Determine Sn of the series 4 + 10 + 16 + 22+...+ (6n - 2).

    I tried to solve this one, but when I did, the n's cancelled out, making it "all real numbers" and since (6n - 2) is the last term, the series isn't infinite.

    PLEASE HELP ME!!! Thanks!
     
  2. jcsd
  3. Sep 9, 2003 #2

    dduardo

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    Staff Emeritus

    1) The series is: [sum] [ x + 2*y] from y = 0 to x-1

    To solve an arithmetic series it is 1/2 times the size of the series times the quanity of the first term plus the second

    Sn = (1/2) * n * ( a1 + a2 )

    the first term you know is the number of terms in the series and the last term is equal to n+2*(n-1) based on the equation.

    So..

    Sn = (1/2) * n * ( n + [ n + 2*(n-1) ] )

    Then you solve Sn = 120

    And you get n = 8 and -7.5

    2) I'm unsure what your asking

    the series is
    [sum] 6x-2 from x=1 to ?

    your saying the series isn't infinite, so what is it?

    if the series goes from x=1 to infinity then the series diverges
     
  4. Sep 9, 2003 #3
    Thanks for the help on the first question. I was assuming the series was finite because (6x - 2) is the last term in the series. Another question: I don't understand how -7.5 can be relevent because it says that n is equal to the number of terms, but there can't be -7.5 terms... can there????
     
  5. Sep 9, 2003 #4
    I think that what the question for is the sum as a function of n.

    Sn = F(n)

    What you would do is write out the summation, and then use the rules that you know to reduce it into a formula.

    For example:

    [sum]c from i=0 to n = cn (c is a constant
    [sum]i from i=0 to n = 1/2(i+1)*i
     
  6. Sep 10, 2003 #5

    dduardo

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    Staff Emeritus

    Astronomer107: -7.5 can occur in a quasi-hyperdimesion manifold, that is forumalated by using the....

    No, you are right, -7.5 isn't an answer. (Only in my imagination)

    Also, what are the choices for question 2.

    Is there an answer: n*(3*n+1)
     
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