A very industrious (but confused) ant is 3 feet up a tree. He decides he can eventually reach the bottom if he follows a schedule. Climb up 1 inch on day ONE, then go down 2 inches per day for two days, then back up 3 inches per day for 3 days, then down 4 inches per day for 4 days, etc. Will the ant ever get down? When, if ever?7
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A very industrious (but confused) ant is 3 feet up a tree. He decides he can eventually reach the bottom if he follows a schedule. Climb up 1 inch on day ONE, then go down 2 inches per day for two days, then back up 3 inches per day for 3 days, then down 4 inches per day for 4 days, etc. Will the ant ever get down? When, if ever?
Direction Day x Distance Net from Starting Point
Up 1 x +1 + 1
Down 2 x –2 + 1 – 4 = – 3
Up 3 x +3 – 3 + 9 = + 6
Down 4 x –4 + 6 – 16 = – 10
Up 5 x +5 –10 + 25 = + 15
Down 6 x –6 + 15 – 36 = – 21
Up 7 x +7 – 21 + 49 = + 28
Down 8 x –8 + 28 – 64 = – 36 reached the ground
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