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Thread: sequence

  1. #1
    Junior Member
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    sequence

    Here is the problem:

    Define a sequence $\displaystyle c_k$ by the rules
    $\displaystyle c_0$ = 2
    $\displaystyle c_1$ = 3
    $\displaystyle c_k = 0.8c_{k-1} - 0.7c_{k-2}$

    Compute $\displaystyle c_2$ through $\displaystyle c_6$


    Anyway, I really struggle with these? Where do I start? What process do I go through? Can someone please walk me through this one problem?

    Thanks
    Last edited by CaptainBlack; Apr 11th 2009 at 10:12 PM.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by relyt View Post
    Here is the problem:

    Define a sequence $\displaystyle c_k$ by the rules
    $\displaystyle c_0$ = 2
    $\displaystyle c_1$ = 3
    $\displaystyle c_k$ = 0.8$\displaystyle c_k-1$ - 0.7 $\displaystyle c_k-2$

    Compute $\displaystyle c_2$ through $\displaystyle c_6$

    Those k - 1 and k-2 should be subscripts

    Anyway, I really struggle with these? Where do I start? What process do I go through? Can someone please walk me through this one problem?

    Thanks
    just plug in the values in the $\displaystyle c_k$ formula

    example, to find $\displaystyle c_2$, plug in $\displaystyle k = 2$, you get

    $\displaystyle c_2 = 0.8c_1 - 0.7c_0 = 0.8(3) - 0.7(2) = 1$

    now find the rest the same way
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by relyt View Post
    Here is the problem:

    Define a sequence $\displaystyle c_k$ by the rules
    $\displaystyle c_0$ = 2
    $\displaystyle c_1$ = 3
    $\displaystyle c_k = 0.8c_{k-1} - 0.7c_{k-2}$

    Compute $\displaystyle c_2$ through $\displaystyle c_6$


    Anyway, I really struggle with these? Where do I start? What process do I go through? Can someone please walk me through this one problem?

    Thanks
    You start by calculating with $\displaystyle k=2$:

    $\displaystyle c_2=0.8c_1-0.7c_0=0.8\times 3 - 0.7 \times 2=1$

    Now you know $\displaystyle c_0,\ c_1,\ c_2$ proceed to calculate $\displaystyle c_3$, and continue from there.

    CB
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  4. #4
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    Got it...thank you. That was a lot easier than I thought
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