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Thread: Finding a recursive formula for a sequence

  1. #1
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    Finding a recursive formula for a sequence

    Hi,

    I have a sequence:

    0, 3, 8, 15, 24

    I believe the general formula for the nth term of the sequence is:

    tn = (n^2) -1

    I cannot figure out what the recursive formula for the sequence is, I appreciate any help.

    Thank you
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  2. #2
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    Re: Finding a recursive formula for a sequence

    $s_{k+1} = (\sqrt{s_k+1}+1)^2 - 1$
    Thanks from jpompey and jonah
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  3. #3
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    Re: Finding a recursive formula for a sequence

    Quote Originally Posted by romsek View Post
    $s_{k+1} = (\sqrt{s_k+1}+1)^2 - 1$
    Ok, I see how that makes sense, would you mind explaining a bit how you arrived at that answer? There aren't any examples in my text that are as complicated as this one.

    Thanks again
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  4. #4
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    Re: Finding a recursive formula for a sequence

    Quote Originally Posted by jpompey View Post
    Ok, I see how that makes sense, would you mind explaining a bit how you arrived at that answer? There aren't any examples in my text that are as complicated as this one.

    Thanks again
    $s_k = k^2 -1,~k=1,2, \dots$

    $k = \sqrt{s_k + 1}$

    $s_{k+1} = (k+1)^2 - 1 = (\sqrt{s_k + 1}+1)^2 - 1$
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  5. #5
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    Re: Finding a recursive formula for a sequence

    $t_n=n^2-1$
    $t_{n-1}=(n-1)^2-1$
    $t_n-t_{n-1}=n^2-1-((n-1)^2-1) $
    $t_n=t_{n-1}+2n-1$
    Thanks from jpompey
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  6. #6
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    Re: Finding a recursive formula for a sequence

    Quote Originally Posted by jpompey View Post
    Hi,

    I have a sequence:

    0, 3, 8, 15, 24

    I believe the general formula for the nth term of the sequence is:

    tn = (n^2) -1

    I cannot figure out what the recursive formula for the sequence is, I appreciate any help.

    Thank you
    Notice that 8- 3= 5, 15- 8= 7, 24- 15= 9, 35- 24= 11, etc. That is, the difference between consecutive terms is odd. t_n- t_{n-1}= 2n- 1 so that t_n= t_{n-1}+ 2n- 1.
    Thanks from jpompey
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  7. #7
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    Re: Finding a recursive formula for a sequence

    Thanks very much everyone
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