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    Calculating a Progression

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    A king in ancient times agreed to award the inventor of chess with one grain of wheat on the first of the 64 squares on a chess board. On the second square the king placed two grains, on the third square he placed 4 grains and on the fourth square he placed 8 grains of wheat. If the amount of wheat continued to double in this manner how many grains of wheat would there be on the 14th square? Also, find the total number of grains of wheat on the board at the time you get to square 14 and tell what their weight is in pounds. (Assume that each grain of wheat weighs 1/7000 of a pound).

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    Solution Preview

    Solution. Denote by a(n) the number of grains in the nth square. Then we have
    a(1)=1, a(2)=2, a(3)=4, a(4)=8, ...

    Solution Summary

    This solution provides steps to find the number of grains of wheat there would be.