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Coursework Task - Number Grids Aim - To investigate the patterns generated from using rules in a square grid. Keywords (Internet Search) - Algebraic expressions, proof, nth terms, sequences Textbook Reference - Key Maths Higher Chapters 4 and 8. Investigate Write up Investigate results from a 2 by 2 square on your chosen grid I have decided to investigate a 2 by 2 square because...................................... After a few results I observed that a .................... Investigate results from a 3 by 3, 4 by 4 square on your chosen grid I decided to try out...................................... I put my results into table and observed that......... I therefore expect........................................ Make a prediction and test I predict that for a 5 by 5 square I will always ........ I tested this by using...................................... Algebraic Proof I will now attempt to prove my results algebraically. I conjecture that......................................... I will use "n" to represent ....................,this means that................................................. Using the rule I get the expressions......and........ By subtracting I get..................................... This proves that........................................... Link results together and extend By putting results...

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