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Math Help - Arithmetic series

  1. #1
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    Arithmetic series

    Struggling a little with this one.

    The fourth term in an arithmetic series is 3k, where k is a constant and the sum of the first six terms of the series is 7k+9

    a) Show that the first term of the series is 9-8k
    b) Find an expression for the common difference of the series in terms of k.

    Given that the seventh term of the series is 12, calculate:

    c) The value of k
    d) The sum of the first 20 terms of the series

    Any help is appreciated, I think if someone just points me in the right direction I should be able to work it out.
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  2. #2
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    Quote Originally Posted by cosine View Post
    Struggling a little with this one.

    The fourth term in an arithmetic series is 3k, where k is a constant and the sum of the first six terms of the series is 7k+9

    a) Show that the first term of the series is 9-8k
    b) Find an expression for the common difference of the series in terms of k.

    Given that the seventh term of the series is 12, calculate:

    c) The value of k
    d) The sum of the first 20 terms of the series

    Any help is appreciated, I think if someone just points me in the right direction I should be able to work it out.
    a)
    t_n = a + (n-1)d

    t_4 = 3k = a + 3d


    S_n = \frac{n[2a + (n-1)d]}{2}

    S_6 = 7k + 9 =3(2a + 5d).


    So you have

    3k = a + 3d and 7k + 9 = 6a + 15d

    Solve them simultaneously.

    Back substitute to answer b).
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  3. #3
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    Lovely stuff, got there and wasn't sure if it would work. thank you very much
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