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# Borders Maths Coursework

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Introduction

## Borders Maths Coursework

Here we are look at what happens when you put a (square) border on each side of the original shape.

Me starting point will have no borders

When I add the borders I put them on each side of the first square and there are 4 borders

Middle

Number of black squares

Number of white squares

1

4

5

8

13

12

25

16

41

20

61

24

Using this I can guess what the next number of white squares will be 20.

A you can see there are 20 white cubes.

This shape has 24 borders

Now

Conclusion

shape I will times 4 by 10 and the number of borders will be 40

Now I will work out the nth term for all the squares in the pictures.

 Number of square 5 13 25 41

1st      2nd        3rd        4th

5    13     25    41

1st8      12      16

2nd    4        4

The nth term for all the cubes is 22n-1.

The 10th number will be worked out by 4 times 10 minus 1 which is 39.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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