Maths Coursework: Consecutive Numbers

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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

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In the above table you can see that each set of consecutive numbers created shows the “Middle number squared” is +1 more than the “First number multiplied by the last”.

From this pattern I will solve it by using algebra. The equation for the “Chosen consecutive numbers” is: n, n + 1, n + 2.

Formula

n, n + 1, n + 2

= (n + 1)² - n(n + 2)

= (n + 1)(n + 1) - (n² + 2n)

= n² + n + n + 1 - (n² + 2n)

= ...

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