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Math Help - Arithmetic series..... other problems..

  1. #1
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    Arithmetic series..... other problems..

    An arithmetic series has first term a and common difference d.
    The sum of the first 31 terms of the series is 310.


    a) Show that a + 15d = 10

    > S31 = 31/2 ( 2a + (31-1) d)
    > 31( a + 15d ) = 310
    > a + 15d = 310/31; a + 15d = 10


    b)Given also that the 21st term is twise the 16th term, find the value of d.

    ???

    c)the nth term of the series is un. Given that
    K
    Sum un = 0, find the value of K.
    n = 1

    ???
    Last edited by CaptainBlack; May 19th 2010 at 08:40 PM. Reason: removed excessive questions
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ansonbound View Post
    An arithmetic series has first term a and common difference d.
    The sum of the first 31 terms of the series is 310.


    a) Show that a + 15d = 10

    > S31 = 31/2 ( 2a + (31-1) d)
    > 31( a + 15d ) = 310
    > a + 15d = 310/31; a + 15d = 10


    b)Given also that the 21st term is twise the 16th term, find the value of d.
    2(a+20d)=a+15d

    so

    a+25d=0

    and you already have:

    a+15d=10

    So solve these simultaneous equations.

    CB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by ansonbound View Post

    c)the nth term of the series is un. Given that
    K
    Sum un = 0, find the value of K.
    n = 1

    ???
    From the previous part you will now know a and b, so plug them into the formula for the sum, which gives a equation in K to solve:

    \sum_{n=1}^K u_n=\frac{K}{2}(2a+(K-1)d)=0

    CB
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