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Math Help - Text Book Error?

  1. #1
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    Text Book Error?

    I'm back with another potential error in the textbook by Chandler/Bostock, Core Course for A Level. Last time it was my mistake, but this time I am more confused:

    Page 594, Question 8

    The sum of the first n terms of a series is given by Sn = n(3n-4). Show that the terms of the series are in arithmetic progression.

    Can this be right?

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  2. #2
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    Re: Text Book Error?

    The test book is correct. You need to prove that the under lying sequence whose sum is given by S_n is in A.P. Did you try considering S_n - S_{n-1}?
    Spoiler:
    Given
    S_n = \sum u_n = n(3n-4). Consider S_n - S_{n-1} = u_n = n(3n-4) - (n-1)(3(n-1)-4) = 6n-5 = 6(n-1)+1
    Similarly we have
    S_{n-1} - S_{n-2} = u_{n-1} = (n-1)(3(n-1)-4) - (n-2)(3(n-2)-4) = 6n-11 = 6(n-2)+1

    So they are in A.P with u_n = 6(n-1)+1 where a=1, d=6
    Last edited by kalyanram; September 11th 2012 at 03:15 AM.
    Thanks from grillage
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    Re: Text Book Error?

    Ok, I can see where I have got confused now. It's one of those horrible oversights that seems silly when you realise. Thanks.
    Last edited by grillage; September 11th 2012 at 03:20 AM.
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  4. #4
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    Re: Text Book Error?

    Actually, to be fair to the book, both cases that I have questioned have turned out to be careless errors from me. I think that is also a normal phenomenon
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