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Math Help - Fibonacci sequence

  1. #1
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    Fibonacci sequence

    Write the first five terms of the sequence defined recursively.

    a1= 28, ak+1= ak -4

    ok i honestly don't understand this at all. i tried to mimic the way the book did it in the example but it did not match the answers in the back of the book. can someone please explain to me how to solve this problem at least give me show me how to do the first two terms. any help is appreciated.
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  2. #2
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    Quote Originally Posted by flexus View Post
    Write the first five terms of the sequence defined recursively.

    a1= 28, ak+1= ak -4

    ok i honestly don't understand this at all. i tried to mimic the way the book did it in the example but it did not match the answers in the back of the book. can someone please explain to me how to solve this problem at least give me show me how to do the first two terms. any help is appreciated.
    Since a_1 = 28, you substitute it into the formula a_{k+1}=a_k-4 to find a_2

     <br />
a_2=28-4 = 24 <br />

    Now your a_k=24, so substitute it in: a_3=24-4 = 20. Hope that helps.
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  3. #3
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    Quote Originally Posted by Roam View Post
    Since a_1 = 28, you substitute it into the formula a_{k+1}=a_k-4 to find a_2

     <br />
a_2=28-4 = 24 <br />

    Now your a_k=24, so substitute it in: a_3=24-4 = 20. Hope that helps.
    i dont understand how you can substitute 28 into the whole equation of ak+1 ?? how is that possible??
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  4. #4
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    Quote Originally Posted by flexus View Post
    i dont understand how you can substitute 28 into the whole equation of ak+1 ?? how is that possible??
    a_k represents "the current value" and a_{k+1} represents the value that comes after your current value. So in this problem you start with a_1 = 28, your initial value is 28. Now you want to find the thing that comes after it (namely a_2). So you use the given formula a_{k+1}=a_k-4, substitute the current value ( a_1 =28 as a_k) to find the succeeding value ( a_{k+1} = a_{2}) and so on...
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  5. #5
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    Quote Originally Posted by Roam View Post
    a_k represents "the current value" and a_{k+1} represents the value that comes after your current value. So in this problem you start with a_1 = 28, your initial value is 28. Now you want to find the thing that comes after it (namely a_2). So you use the given formula a_{k+1}=a_k-4, substitute the current value ( a_1 =28 as a_k) to find the succeeding value ( a_{k+1} = a_{2}) and so on...
    its clear like water now thank you.
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