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Thread: how to determine the general term

  1. Apr 8th 2010, 10:40 AM #1
    needhelpplease1
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    how to determine the general term

    #1: Determine the general term, tn, for sequence/series 64, -16, 4, -1,...

    I have no idea how to do this
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  2. Apr 8th 2010, 10:53 AM #2
    mathemagister
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    Quote Originally Posted by needhelpplease1 View Post
    #1: Determine the general term, tn, for sequence/series 64, -16, 4, -1,...

    I have no idea how to do this
    Here's a clue: notice how each term is -1/4 times the previous term. This, and your notes, should help you find the answer.
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  3. Apr 8th 2010, 10:54 AM #3
    harish21
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    Quote Originally Posted by needhelpplease1 View Post
    #1: Determine the general term, tn, for sequence/series 64, -16, 4, -1,...

    I have no idea how to do this

    a_{n+1} = \frac{-a_n}{4}

    Note: This is the recurrence relation.

    The series is expressed as what mathemagister has stated:

    {a_n} = [-(-1)^n] 4^{4-n}
    Last edited by harish21; Apr 8th 2010 at 11:20 AM.
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  4. Apr 8th 2010, 10:58 AM #4
    mathemagister
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    And that translates to a_n = -(-1)^n 4^{4-n}
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  5. Apr 8th 2010, 11:07 AM #5
    needhelpplease1
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    hmm..

    Quote Originally Posted by mathemagister View Post
    And that translates to a_n = -(-1)^n 4^{4-n}
    wait, wouldn't it be tn = 64(-1/4)^n?
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  6. Apr 8th 2010, 11:11 AM #6
    mathemagister
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    Quote Originally Posted by needhelpplease1 View Post
    wait, wouldn't it be tn = 64(-1/4)^n?
    No, because then when n = 1, you wouldn't get 64.

    EDIT: I think you were thinking of t_n = 64(-1/4)^{n-1} which is also a correct way to express the sequence.

    Hope everything is clarified

    Mathemagister
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