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# Number Grid.

Extracts from this document...

Introduction

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.

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

Middle

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 inOpposite 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.

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

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

3 x 4

3 x 5

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

20                20                20                20

The nth  term is 20(n-1)

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