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Number Grid.

Extracts from this document...

Introduction

image00.png

I have been given a 10 by 10 grid, with a 2 by 2 box going around numbers 12, 13, 22 and 23, as shown below.

image21.png

I have been asked to find the product of the top right number and the bottom left number in the box (2 by 2 box). Then I was told to do the same with the top left number and the bottom right number. After that I had to calculate the difference between these products.

13 x 22  =  286 _

12 x 23  =  276

        10

...read more.

Middle

image11.pngimage10.pngimage11.pngimage10.pngimage10.pngimage11.pngimage11.png

We know that the nth  term will have to be squared. We know this by the second difference is all the same.

Term (n)……

1

2

3

4

5

Differences in

Opposite corners……

0

10

40

90

160

Term (n) squared…

1

4

9

16

25

I have found the rule.  nth term squared x ten = n+1. to make it simpler I’ll put it in algebraic form, 10(n-1)²

I would now like to find out if this will be the same for rectangles.

...read more.

Conclusion

Results:

Term (n)

1

2

3

4

5

6

7

Differences in opposite

corners

0

10

20

30

40

50

60

Term (n)……                1                2                3                4                5                6                

Differences in

Opposite corners        0                10                20                30                40                50

image11.pngimage11.pngimage10.pngimage10.pngimage11.pngimage10.pngimage11.pngimage10.pngimage11.pngimage10.png

        10                10                10                10                10

The nth  term is 10(n-1)

Does this rule work with other rectangles?

I believe I shall require only one example of each and will proceed on this principle. I will also be changing the layout to make it easier.

3 x X

3 x 3

image24.png

3 x 4

image19.png

3 x 5

image20.png

Results:

Term (n)

1

2

3

4

5

Differences in opposite

corners

0

20

40

60

80

Term (n)……                1                2                3                4                5                                

Differences in

Opposite corners        0                20                40                60                80                

image11.pngimage10.pngimage11.pngimage10.pngimage11.pngimage10.pngimage11.pngimage10.png

        20                20                20                20                

The nth  term is 20(n-1)

...read more.

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