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Maths coursework i am going to investigate a pattern by taking a squares and rectangles and multiplying the top corners. For squares 2x2, 3x3, 4x4, 5x5 for rectangles 2x3,24,2x5,3x2,3x4,3x5,4x2,4x3,4x5 i will be doing this in a nine squared grid and a ten squared grid after my results if there is a pattern i will make a formula to describe the pattern 2x2 squares on 10 squared grid. 16 26 15 25 16x25=400 400-390=10 15x26=390 59 60 49 50 59x50=2950 2950-2940=10 49x60=2940 3x3 22 23 24 32 33 34 42 43 44 22x44=968 1008-268=40 24x42=1008 27 28 29 37 38 39 47 48 49 27x49=1323 1363-1323=40 47x29=1363 Algerbraic equation. Key G= grid size N= number w= number of squares. 2x2 sqaure on a 10 size grid n n+(w-1) n+g n+(w-1)+g 3x3 sqaure on a 10 size grid n n+(w-2) n+(w-1) n+g n+(w-2)+g n+(w-1)+g n+2g n+(w-2) +2g n+(w-1)+ 2g I can simpifly this into a forumula G(n-1)² and i realise i have 2 varibles that can be changed the number of sqaures grid size RESULTS Size of squares Difference between answers 2x2 10 3x3 40 4x4 90 5x5 160 From these results i can conclude that the formula for this pattern (when n is the number in and G equals grid...

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