# As part of my coursework I have chosen number grid.

Extracts from this document...

Introduction

As part of my coursework I have chosen number grid.

According to the task, I followed four steps in 10 10 grid

- A box is drawn round four numbers.
- Find the product of the top left number and the bottom right number.
- Do the same with the top right and bottom left number.
- Calculate the difference between these numbers.

The results are noted in the table below.

BOX | MULTIPLIED NUMBER | PRODUCT | DIFFERENCE |

4 5 | 4 15 | 60 | 10 |

14 15 | 5 14 | 70 | |

26 27 | 26 37 | 962 | 10 |

36 37 | 27 36 | 972 | |

81 82 | 81 92 | 7452 | 10 |

91 92 | 91 82 | 7462 |

From the worked examples I find that the difference between the product found for the diagnol square in the 10 10 is 10.

From these results I predict that the difference between the next products in a diagnol square of 2 2 will be 10in 10 10 grid.

BOX | MULTIPLIED NUMBER | PRODUCT | DIFFERENCE |

31 32 | 31 42 | 1302 | 10 |

41 42 | 32 41 | 1312 | |

66 67 | 66 77 | 5082 | 10 |

76 77 | 67 76 | 5092 | |

89 90 | 89 100 | 8900 | 10 |

99 100 | 90 99 | 8910 |

Middle

4 37

148

90

24 25 25 26

7 34

238

34 35 36 37

21 22 23 24

31 32 33 34

21 54

1134

90

41 42 43 44

24 51

1224

51 52 53 54

56 57 58 59

66 67 68 69

56 89

4984

90

76 77 78 79

59 86

5074

86 87 88 89

The results show that the difference between the products in 4 4 square is 90.It is five times to the difference in 3 3 square.I predict that it will be true for next squares in 4 4 square in 10 10 grid.

BOX | MULTIPLIED NUMBER | PRODUCT | DIFFERENCE |

7 8 9 10 | |||

17 18 19 20 | 7 40 | 280 | |

27 28 29 30 | 10 37 | 370 | 90 |

37 38 39 40 | |||

33 34 35 36 | |||

43 44 45 46 | 33 66 | 2178 | |

53 54 55 56 | 36 63 | 2268 | 90 |

63 64 65 66 | |||

46 47 48 49 | |||

56 57 58 59 | 46 79 | 3634 | 90 |

66 67 68 69 | 49 76 | 3724 | |

76 77 78 79 |

The results show that the prediction was right.

What would be the difference in 5 5 square in this grid ?

BOX | MULTIPLIED NUMBER | PRODUCT | DIFFERENCE |

4 5 6 7 8 | |||

14 15 16 17 18 | |||

24 25 26 27 28 | 4 48 | 192 | 160 |

34 35 36 37 38 | 8 44 | 352 | |

44 45 46 47 48 | |||

11 12 13 14 15 | |||

21 22 23 24 25 | |||

31 32 33 34 35 | 11 55 | 605 | 160 |

41 42 43 44 45 | 15 51 | 765 | |

51 52 53 54 55 | |||

26 27 28 29 30 | |||

36 37 38 39 40 | |||

46 47 48 49 50 | 26 70 | 1820 | |

56 57 58 59 60 | 30 66 | 1980 | 160 |

66 67 68 69 70 |

The difference between the products is 160.

Conclusion

THE SEQUENCE OF NUMBERS: 10, 40, 90, 160,

Position Number | 1 | 2 | 3 | 4 |

Term | 10 | 40 | 90 | 160 |

Difference | 30 | 50 | 70 | |

2nd Difference | 20 | 20 |

The 2nd difference between the succesive terms is (+)20.So the nth term will be

DINO

Nth term = 20n – 10

=10

4th term = 20 4 – 10

= 80 –10

= 70

5th term = 20 5 – 10

= 100 – 10

= 90

10th term = 20 10 – 10

= 200 – 10

= 190

BOX | MULTIPLIED NO | PRODUCT | DIFFERENCE |

x x + 1 | x(x + 11) | x + 11 | 10 |

x + 10 x + 11 | (x + 1) (x + 10) | x + 10x + x +10 | |

3 3 SQUARE | |||

x x + 1 x + 2 | x(x + 22) | x + 22x | |

x + 10 x +11 x + 12 | (x + 2) (x + 20) | x +22x +2x + 40 | 40 |

x +20 x + 21 x + 22 | |||

4 4 SQUARE | |||

x x + 1 x + 2 x + 3 | |||

x + 10 x + 11 x + 12 x + 13 | x(x + 33) | x + 33x | |

x + 20 x + 21 x + 22 x + 23 | (x + 3) (x + 30) | x +30x + 3x + 90 | 90 |

x + 30 x +31 x + 32 x + 33 | |||

x x + 1 x + 2 x + 3 x + 4 | |||

x +10 x + 11 x + 12 x + 13 x + 14 | x(x + 44) | x + 44x | |

x +20 x +21 x + 22 x + 23 x + 24 | (x + 4) (x +40) | x + 40x +4x + 160 | 160 |

x + 30 x + 31 x + 32 x + 33 x + 34 | |||

x +40 x + 41 x + 42 x + 43 x + 44 |

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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