Warm Up: Introducing Geometric Sequences
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Warm Up |
Introducing Geometric Sequences
The Chessboard Problem, Part I
A father and daughter sit down to a game of chess. The father, frustrated by the lack of cleanliness of his daughter’s room, proposes a deal. Picking up 1 penny, he places it on the first square on the chessboard and says he will pay her 1 penny for the first day she cleans her room. He lays down 2 pennies on the next square and says he will pay her 2 pennies for the second day she cleans her room. On the third square, he lays down 4 pennies, and explains that every day that she cleans her room she will earn double the amount she earned on the previous day.
Staring at the 7 pennies on the board, the daughter rolled her eyes and said no to the deal. Did the daughter make a wise decision? How much would she have earned after 10 days? 15 days? 32 days? 64 days? Note there are 64 squares on a chessboard.
A father and daughter sit down to a game of chess. The father, frustrated by the lack of cleanliness of his daughter’s room, proposes a deal. Picking up 1 penny, he places it on the first square on the chessboard and says he will pay her 1 penny for the first day she cleans her room. He lays down 2 pennies on the next square and says he will pay her 2 pennies for the second day she cleans her room. On the third square, he lays down 4 pennies, and explains that every day that she cleans her room she will earn double the amount she earned on the previous day.
Staring at the 7 pennies on the board, the daughter rolled her eyes and said no to the deal. Did the daughter make a wise decision? How much would she have earned after 10 days? 15 days? 32 days? 64 days? Note there are 64 squares on a chessboard.
