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Math Help - Help with Explicit Sequence Formula

  1. #1
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    Help with Explicit Sequence Formula

    Write a possible explicit rule for each sequence, and find the 10th term.

    16, 4, 1, 1/4, 1/16


    I know that the recursive formula is a_n = 1/4a_n-1, but I don't know how to make an explicit formula.
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  2. #2
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    Quote Originally Posted by bfbcool2 View Post
    Write a possible explicit rule for each sequence, and find the 10th term.

    16, 4, 1, 1/4, 1/16


    I know that the recursive formula is a_n = 1/4a_n-1, but I don't know how to make an explicit formula.
    A term in a geometric series is given by:

     T_n = ar^{n-1} where a is the first term, and r is the ratio between any two consecutive terms. You have already found the ratio in your recursive formula.
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  3. #3
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    I figured it out.

    The formula is A_n = 1/4^(n-1) +16

    N = the Sequence number (1, 2, 3, 4, etc.)
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  4. #4
    MHF Contributor harish21's Avatar
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    a_n = 4^{3-n}

    for n = 1,2,....
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