Maths Coursework: Consecutive Numbers

... MARTIN GALLAGHER Maths Coursework: Consecutive Numbers Introduction In this coursework I am trying to find a common pattern in consecutive numbers, and then solve the pattern with algebra. Problem 1: Write down three consecutive numbers. Square the middle number; multiply the first number by the third. Compare your answers, what do you notice? Problem 2: Write down two consecutive numbers. Square both of the numbers and find the difference between the two squares, what do you notice? Problem 3: Write down five consecutive numbers. Square the middle number; multiply the first number by the fifth. Compare your answers, what do you notice? Problem 4: Write down three consecutive numbers but this time with a gap between them, like this: 1, 3, 5. Square the middle number; multiply the first number by the third. Compare your answers, what do you notice? Problem 1 Chosen consecutive numbers Middle number squared First number multiplied by the last. Difference 9, 10, 11 5, 6, 7 7, 8, 9 10, 11, 12 18, 19, 20 100 36 64 121 361 99 35 63 120 360 1 1 1 1 1 In the

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