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A chessboard has 64 squares. George places 1 grain of rice on the first square, 2 grains on the second square, 4 grains on the third square, 8 grains on the fourth square, and so on, until he has placed grains of rice on 10 squares. Once George has put rice on the 10th square, he has placed a total of (how many) grains of rice on the chess board.

Answer :

genna123
The number of grains on the Nth square Is 2^(N-1). There are 512 grains on the 10th square alone, and 1,023 of them on all 10 squares together.

Answer: There are 1023 grains on 10 squares in total.

Step-by-step explanation:

Since we have given that

Number of grains on first square = 1

Number of grains on second square = 2

Number of grains on third square = 4

Number of grains on fourth square = 8

Since it forms a geometric sequence :

1,2,4,8,......................

So, we need to find the number of squares on 10 th square:

So, here, a = 1

r = 2

n = 10

[tex]S_{10}=\dfrac{a(r^{n-1})}{r-1}\\\\S_{10}=\dfrac{1(2^{10-1})}{2-1}\\\\S_{10}=1024-1\\\\S_{10}=1023[/tex]

Hence, there are 1023 grains on 10 squares in total.

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