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anonymous

  • one year ago

The following function defines a recursive sequence: f(0) = -5 f(1) = 20 f(n) = -4•f(n -1) - 3•f(n - 2); for n > 1 Which of the following sequences is defined by this recursive function? -5, -20, -65, -200, … -5, 20, -92, 372, … -5, -24, -92, -372, … -5, 20, -65, 200, …

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  1. freckles
    • one year ago
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    you are given the first two terms in the sequence -5,20,... so you can definitely eliminate one of those choices anyways to find the third replace n with 2

  2. anonymous
    • one year ago
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    okay, so what is the next step?

  3. freckles
    • one year ago
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    replacing n with 2

  4. freckles
    • one year ago
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    then using that f(0)=-5 and f(1)=20 to find f(2) (which is the third term)

  5. anonymous
    • one year ago
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    I eliminated A and C. So I am left with B or D.

  6. anonymous
    • one year ago
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    I'm not sure what the third term is.

  7. freckles
    • one year ago
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    it is f(2)

  8. freckles
    • one year ago
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    since f(0) is first term and f(1) is second so f(2) is the third

  9. freckles
    • one year ago
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    that is why I'm asking you to replace n with 2

  10. anonymous
    • one year ago
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    oh okay.

  11. anonymous
    • one year ago
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    Don't if I plug in the -5 and the 20 into the term won't I get -65? That is what I got at first but I'm not sure if that is right?

  12. freckles
    • one year ago
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    \[f(n) = -4•f(n -1) - 3•f(n - 2) \\ f(2)=-4 \cdot f(2-1)-3 \cdot f(2-2) \\ f(2)=-4 \cdot f(1)-3 \cdot f(0)\] remember f(1) is 20 and f(0) is -5 so you have \[f(2)=-4 \cdot 20-3 \cdot (-5)\] and yes -80+15=-65

  13. freckles
    • one year ago
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    so your work is done now you can move on to next problem good job

  14. anonymous
    • one year ago
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    oh okay, so that would mean if I continued with the process I would ghet 200 next right?

  15. freckles
    • one year ago
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    if you don't get 200 then none of the choices are correct :p

  16. anonymous
    • one year ago
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    I did get 200, so it is D. Thanks so much! Can you help me with a few more?

  17. freckles
    • one year ago
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    sure

  18. freckles
    • one year ago
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    one more I think

  19. anonymous
    • one year ago
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    Okay I'll tag you.

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