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Math Help - Geometric Sequences - How to find maximum value

  1. #1
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    Geometric Sequences - How to find maximum value

    This question legitimately confuses me.

    I found that the formula for a geometric sequence is An=1800 x 0.9^(n-1)

    How does one calculate the maximum value from that, however?
    I do not understand how there is a maximum value for geometric sequences.
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  2. #2
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    Re: Geometric Sequences - How to find maximum value

    I think you mean a value which the sum of the sequence approaches but never reaches, called the sum to infinity. The formula ia a/(1-r)
    So in your case a=1800 and r=0.9 so sum to infinity =1800/0.1 =18000. r has to be between -1 and +1 for a sequence to have a sum to infinity.
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  3. #3
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    Re: Geometric Sequences - How to find maximum value

    The maximum value of a_n is simply the first term (assumed to be a_1 = 1800), because all proceeding terms get smaller.
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