A machine is driving a 4.5 foot post into the ground. The first hit drives the post 16 inches into the ground. The second hit drives the post 12.8 inches further into the ground. If successive distances the machine drives the post into the ground form a geometric sequence and the machine is left to run forever, how far, to the nearest inch, will the post be driven into the ground? inches

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A: Please see the below picture for detailed solution.

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