One gram of wheat on the first of 64 squares of a chess board . On the second sq

Question

One gram of wheat on the first of 64 squares of a chess board . On the second square two grams of wheat , on the third square four grams of wheat , on the fourth square eight grams of wheat , the amount doubled for each remaining square, how many grains of wheat should be placed on square 14 ? Also the total number of grains of wheat on the board at the time and their total weight in pounds . (Assume that each grain weights 1/7000 pound) One gram of wheat on the first of 64 squares of a chess board . On the second square two grams of wheat , on the third square four grams of wheat , on the fourth square eight grams of wheat , the amount doubled for each remaining square, how many grains of wheat should be placed on square 14 ? Also the total number of grains of wheat on the board at the time and their total weight in pounds . (Assume that each grain weights 1/7000 pound)

Explanation / Answer

It is the case of geometric progression. know that if the 1st term of a series is a and if the common ratio between the successive terms is r, then the nth term of such a geometric series is arn-1.

Here, a = 1 and r = 2 so that, the number of grams of wheat on the 14th square is 1*214-1 = 213 = 8192 grains.

The sum (Sn) of the first n terms of a geometric progression is given by the formula Sn = a(1-rn)/(1-r) ( if r 1), and a and r are as above.

Here, n = 64,a = 1 and r = 2 so that the weight of the wheat on the chessboard is 1(1-264)/(1-2) = 264 -1 grains = (264 -1)/7000 pounds.

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