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  • Level: GCSE
  • Subject: Maths
  • Word count: 2022

Number Stairs

Extracts from this document...

Introduction

Number Stairs

1+2+3+11+12+21=50

8+9+10+18+19+28=92

48+49+50+58+59+68=332

71+72+73+81+82+91=470

15+16+17+25+26+35=161

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81

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71

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61

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51

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41

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10

This is the stairs numbers and I add all the stair number and every time I got different totals. E.g. 50, 92, 332, 470 and 161

91

92

93

94

95

96

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98

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100

81

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71

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61

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71+72+73+81+82+91=470

72+73+74+82+83+92=476

73+74+75+83+84+93=482

74+75+76+84+85+94=488

I am finding out different totals, but going up by set amount.

Every time it goes up by 6.

Stair Number:  71                      72                         73                         74

Stair total:      470                         476                        482                         488                

Difference:                     6                           6                               6

Now I know this pattern I can predict that the stair total for stair 75 will be 492 as 488+6.

To make sure that is right I have to test prediction.

75+76+77+85+86+95=494                 my predict is right

We can therefore say that every time you move the stair shape one square to the right you increase the stair total by 6 and every time you move the stair shape one square to the left you decrease the stair total by 6.

72 + 73 + 74 + 82  +  83 +    92 = 476

72  72+1 72+2 72+ 10 72+11 72+20

         1 + 2  +   10 +   11  +   22  = 44

72x6+44=476

This is the formula  

...read more.

Middle

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31+32+33+41+42+51=230

32+33+34+42+43+52=236

33+34+35343+44+53=242

I am predicting the next one that start with 34 the answer is going to be 248 to find out I am right I have to work it out.

34x6+44=248

N=34

34 + 35 + 36 + 44 + 45 + 54  =248

N   n+1  n+2  n+10  n+11 n+20=6n+44   change 34 to N

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8+9+10+18+19+28=92

18+19+20+28+29+38=152

28+29+39+38+39+48=212

38+39+40+48+49+85=272

Every time it goes up by 60.

...read more.

Conclusion

We can now say that in order to find the equation for an 11 by 11 number grid all we have to do is add 4 to the equation of a 10 by 10 grid. If we do this then the equation will be 6x + 48 = stair total.

I am now going to check this equation with stair 12 on an 11 by 11 number grid.

34

23

24

12

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14

6x + 48 = stair total

(6 x 12) + 48 = 120

12 + 13 + 14 + 23 + 24 + 34 = 120

This is true so I conclude that the stair total for any 3-step stair on an 11 by 11 number grid is 6x + 48= stair total.

We can now say that every time you increase the size of the grid by one (going from a 9by9 number grid to a 10by10 number grid) you have to add four more to the equation. Therefore if you decrease the size of the grid by one you must also decrease the equation by 4.

With this knowledge I can now find a general equation for any 3-step stair on any size grid.

Grid Size                Formula

7 by 7                         6x + 32

8 by 8                         6x + 36

9 by 9                         6x + 40

10 by 10                 6x + 44

11 by 11                 6x + 48

Masood Akbari 11.6HA                                                                                       page

...read more.

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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