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Dominik Borgolte Buckswood School GCSE Mathematic coursework "Step stairs" Centre number: Candidate number: 2776 Introduction I am going to investigate formulas that can be used to calculate the sum of the number in a staircase on a grid paper. In my investigation I will use: St: stand for stair total ( S stand for stair and t for the total sum ) g: stand for the size of the grid (e.g. in 12x12 grid n=12) n: stand for stair number, which is always the bottom left number x. stand for the size of the stairs ( e.g. a 6 step stair would be x=6 ) 3 step stair on a 10x10 grid ( 1 ) I want to find a formula, which makes it easier for me to calculate the total size of a 3 step stair in a 10 x 10 grid. 10 x 10 grid 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 31 32 33 34 35 36 41 42 43 44 45 46 47 48 49 50 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 19 20 21 22 23 24 21 22 23 24 25 26 27 28 29 30 13 14 15 16 17 18 11 12 13 14 15 16 17 18 19 20 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 St: 1+2+3+11+12+21=50 I have added all the squares of the 3 step stairs together, which gives me...

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