Ethan wants to recreate the story of the rice and the chessboard, but he only has a mancala board (which has 1414 spaces). If he puts 11 grain of rice in the first space of the mancala board, 22 on the second, 44 on the third, and so on, doubling the amount for each space, how many total grains of rice will be on the board?

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parmesanchilliwack parmesanchilliwack · Answer 1 · 2019-01-17T10:47:30+01:00

Answer: 16,383

Step-by-step explanation:

According to the question,

The total spaces a mancala board = 14

In the first space, number of grain of rice = 1

In second space number of grain of rice = 2

In third space number of grain of rice = 4

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ So on,

Thus, We obtained a GP,

1 , 2, 4, 8, -----------

Where total number of terms, n= 14

First term, a = 1, Common ratio, r = 2

Thus, the sum of the above GP,

[tex]S_{14} =\frac{1(2^{14}-1)}{(2-1)}[/tex]

[tex]S_{14} =\frac{16384-1}{2-1}[/tex]

[tex]S_{14} =\frac{16383}{1}[/tex]

[tex]S_{14} =16383[/tex]

Thus, The total numbers of grain of rice in the board = 16,383