Coursework.Info - Inspiration in an Instant

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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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 The value of the rectangle is 132. We would get the value by calculating the sum of all the numbers. A way we could find this value out could be by using a formula. But what formula could we use? n n+1 n+2 n+10 n+11 n+12 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 The sum of the values in the turquoise box adds up to 132. To find this, we could try n and n+12. 16+16+12=44 132?44=3 3 are equal to the width. So far we have w (2n + 12). To see if the formula w (2n+12) works, we will try it out using the rose coloured box. 42+43+44+52+53+54= 288. Width= 3. 3(2(42) +12): 3(84+12): 3(96). 3x96=288. Once again, 76+77+78+86+87+88=492. Width=3. 3(2(76) +12): 3(152+12): 3(164) 3x164=492. This formula so far works. But what would happen if the width changed? 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 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 This time, the width of each shaded square is 4. For the first shaded square, the values come up to 180. 4(2n+12): 4(44): 4x44= 176. As you can see, we have changed the width, but have not changed the n+12 to n+13. If we tried...

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