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Math Help - Sequences and Series

  1. #1
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    Sequences and Series

    Show that 28, 23, 18, 13....... is arithmetic and hence find un and the sum of sn of the first n terms in simplest form.


    I got un=23+5n and sn=n/2(51+5n)
    but the answers in the book are:
    un=33-5n and sn=n/2(61-5n)
    so i dont know where I went wrong
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  2. #2
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    Hello, juliak!

    Show that 28, 23, 18, 13, \hdots is arithmetic
    and hence find u_n and the sum S_n of the first n terms.

    The first term is: . u_1 = 28

    The common difference is: . d = -5


    The n^{th} term is: . u_n \:=\:u_1 + (n-1)d

    So we have: . u_n \:=\:28 + (n-1)(-5)\quad\Rightarrow\quad\boxed{ u_n \:=\:33-5n}


    The sum of the first n terms is: . S_n \;=\;\frac{n}{2}\bigg[2u_1 + (n-1)d\bigg]

    So we have: . S_n \;=\;\frac{n}{2}\bigg[2(28) + (n-1)(-5)\bigg] \quad\Rightarrow\quad\boxed{ S_n \;=\;\frac{n}{2}(61-5n)}

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