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Math Help - Recursively defined functions

  1. #1
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    Recursively defined functions

    Can someone help me get started with this...

    Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined recursively by f(0)=3 and for n=0,1,2,...
    f(n+1)=-2f(n)

    I'm not looking for the answer, but for help in understanding.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by sjenkins View Post
    Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined recursively by f(0)=3 and for n=0,1,2,...
    f(n+1)=-2f(n)

    I'm not looking for the answer, but for help in understanding.
    We're given \begin{cases}f(0)=3\\f(n+1)=-2f(n) \end{cases}. To find f(1) choose n such that n+1=1. This gives n=0. Then use the relation f(n+1)=-2f(n) with n=0 : f(0+1)=-2f(0)\implies f(1)=-2\times 3=-6. Does it help ?
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  3. #3
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    I still feel so confused, but maybe if I give an example that is given in the book, I will understand what is going on.

    Suppose that f is defined recursively by
    f(0)=3
    f(n+1)=2f(n)+3
    Find f(1), f(2), f(3), f(4)

    Solution:
    f(1)=2f(0)+3=2X3+3=9
    f(2)=2f(1)+3=2X9+3=21

    Where does that 9 come from????
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by sjenkins View Post
    Solution:
    f(1)=2f(0)+3=2X3+3=9
    f(2)=2f(1)+3=2X9+3=21

    Where does that 9 come from????
    That's the value of f(1). f(2) is given by f(2)=2{\color{red}f(1)}+3 and has f(1) has been computed just before, we know that it equals 9.
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  5. #5
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    Ohhhhh....that makes complete sense. I knew I was just missing something simple.

    Thanks again for the help!!
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