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Thread: 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 $\displaystyle 28, 23, 18, 13, \hdots$ is arithmetic
    and hence find $\displaystyle u_n$ and the sum $\displaystyle S_n$ of the first $\displaystyle n$ terms.

    The first term is: .$\displaystyle u_1 = 28$

    The common difference is: .$\displaystyle d = -5$


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

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


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

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

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