# 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 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.

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)

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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