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Math Help - Arithmetic and Geometric Sequences

  1. #1
    Junior Member VDestinV's Avatar
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    Arithmetic and Geometric Sequences

    Here is the question:

    In an old story, a king asked a peasant to come and work for him. They both agreed that the job to be done could be completed in a month (30 days). The peasant asked the king if he could be paid in the following way: "On the first day that I work, I would like to be paid one penny. Each day that I work, I would like you to double my income." The king thought this was a great deal and happily agreed.

    Analyze the deal that the king and the peasant made to determine whether or not the peasant made a good deal with the king.

    Now I know that the peasant is getting the better deal. And I believe I have to use the formula tn=ar^n-1.

    Help please?
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    You're correct. The formula is 2^{n}-1

    For instance, how much on the 5th day?. 16+8+4+2+1=31

    2^{5}-1=31

    So, on the 30th day, he would have 2^{30}-1.

    A rather large number, even in pennies.

    That is $10,737,418.23

    The king may have him beheaded after seeing that.
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