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Algebra coursework Rotten [square] apples For our algebra coursework we were asked to investigate a certain task. The task that I was given was called Rotten [square] apples and is described as follows. A rotten square apple is placed in a barrel of square apples. Each day, any apple touching the rotten apple goes rotten! I started the investigation by working out how many rotten apples there were by the end of the first five days and I recorded it in a table. Day (n) 1 2 3 4 5 Number or rotten [square] apples 1 5 13 25 41 After that I worked down the table, working out the differences which would enable me to work out the number of rotten apples on any given day. Day (n) 1 2 3 4 5 Number of rotten apples 1 5 13 25 41 1st difference 4 8 12 16 2nd difference 4 4 4 Because the 2nd differences are the same I now know that this is a quadratic sequence. For a linear sequence the equation is half the 2nd difference n². As 4 is the number shown I...

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