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Matthew Russell Maths Coursework T-Total Using a 9 by 9 grid, a 'T' shape was made covering 5 numbers. The grid is shown below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 All the numbers in this 'T' shape added together make a total of 37, (1+2+3+11+20=37). This total is known as the "T-total". The number at the bottom of this T-shape (20) is known as the T-number. To investigate if there was any relationship between the T-total and the T-number, the T-shape was translated onto different positions on the grid. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 T-number 20 21 22 23 T-total 37 42 47 52 T-number 24 25 26 27 T-total 57 62 67 72 T-number 28 29 30 31 T-total 77 82 87 92 T-number 32 33 34 35 T-total 97 102 107 112 T-number 36 37 38 39 T-total 117 122 127 132 This shows that whenever the T-number moves up by 1, the T-total number goes up by 5. This is because there are 5 numbers in each T-shape. Next we will find a pattern that will connect the T-number to the T-total which is called the nth term. First of all, the T-totals are going up by 5 each time. If we take the first T-shape ( red ) as an example, the T-number...

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