Question

If i place 1 cent on the first square of a chess board, 2 cents on the second, and then double it on each square, how much money will be placed on the 18th square

Answer 1

First square = 1 cent

Second square = 2 cents

The coins are doubled on the next square:

1st square = 1

2nd square = 1 x 2 = 2

3rd square = 1 x 2² = 4

4th square = 1 x 2³ = 8

therefore the nth square = 1 x 2⁽ⁿ⁻¹⁾

nth square = 2⁽ⁿ⁻¹⁾

Find the 18th square:

18th square = 2⁽¹⁸⁻¹⁾

18th square = 2¹⁷

18th square = 131,072

Answer: There are 131,072 cents on the 18th square

Answer 2

hey!

here is answer

1 st square = 1cent

2nd square=2 cents

coins doubled

1st square=1

2nd square=1*2=2

3rd square=1*2^2=4

4th square=1*2^3=8

therefore nth square = 1*2^(n-1)

2^(n-1)

hence 18 th square

= 2^(n-1)


= 2^(18-1)

2^17

= 131072.

hope it helps

thanks