Maths Sequences Investigation

GCSE Maths

Maths Coursework

Firstly I drew out a series of patterns so I could study the many different aspects of them. Here is what I found:

The number of Black Squares increases each time by the number of white squares.

The number of White squares increases in multiples of four every time

The total squares equals the sum of Black Squares and White Squares

The diameter increases by two every time

Because this sequence of patterns follows a sequence and increases by some set amount each time I can assign a Pattern Number or ‘N’ as an integer to increase by one every pattern. Here is another table but showing N:

Now I can use n as a basis for building equations used to define the different aspects such as the ones in the table above. Here is the equation for the number of white squares:

4 x N = the number of white squares

4N = W

And I also worked out the equation for the Diameter of any pattern:

2 x N + 1 = the diameter of the pattern

2N+1 = D

These two equations were relatively easy to work out because they follow a set increment. I simply looked down the table above and noted down the difference in them:

Forming an equation for the total number of squares is slightly harder. Now I will explain how I worked it out:

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