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# Number Stairs Investigation

Extracts from this document...

Introduction

Number Stairs

...read more.

Middle

26

27

28

29

30

11

12

13

14

15

16

17

18

19

20

1

2

3

4

5

6

7

8

9

10

 lowest number (n) Long operation Total (t) 1st Difference (D0) 1 1 + 2 + 3 + 11 + 12 + 21 50 6 2 2 + 3 + 4 + 12 + 13 + 22 56 6 3 3 + 4 + 5 + 13 + 14 + 23 62 6 4 4 + 5 + 6 + 14 + 15 + 24 68 6 5 5 + 6 + 7 + 15 + 16 + 25 74 6

Judging by this, the first part of the overall equation for a 3 step stair is 6n +?

 n 6n T D0 1 6 50 44 2 12 56 44 3 18 62 44 4 24 68 44 5 30 74 44
...read more.

Conclusion

s=0, T=0, d=0

s=1, T=0, a + b + c=0

s=2, T=1, 8a + 4b + 2c = 1

s=3, T=4, 27a + 9b + 3c = 4

s=4, T=10, 64a + 16b + 4c =10

T= 0.1666(s³) + 0(s²)-0.1666s-0

T= 0.1666(s³) - 0.1666s

...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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# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Number stairs

the terms added in the second portion of the 5-step stair is: T= X + (x+6n) + (x+4n+8) + (x+4n+7) + (x+3n+6) + (x+3n+5) + (x+3n+4) + (x+2n+4) + (x+2n+3) + (x+2n+2) + (x+2n+1) + (x+n+2) + (x+n+1) + (x+n) + (x+9) + (x+8) + (x+1) + (x+2) + (x+3)

2. ## Step-stair Investigation.

X = 6X. 2 As you can see in my results on past pages show that the number of Xs in a 3 step-stair = 6. This proves that this starting formula works. The second thing I realised was that the bits below coloured red always stayed the same, and equal in value.

1. ## For other 3-step stairs, investigate the relationship between the stair total and the position ...

49 57 58 59 60 61 12 Formula: 15x-200 23 24 1: 15x56-200= 640 34 35 36 2: 12+23+34+45+56+24+35+46+57+36+47+58+48+59+60= 640 45 46 47 48 56 57 58 59 60 18 Formula: 15x-220 30 31 1: 15x66-220= 770 42 43 44 2: 30+42+54+66+43+55+67+56+68+69+18+31+44+57+70= 770 54 55 56 57 66 67 68

2. ## Number Grid Investigation

I am now going to change the size of my 10 x 10 grid, I will change It to an 8 x 8 grid. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1. ## My Investigation is called 'Number Stairs'

22 23 24 25 26 27 28 29 30 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 8 9 10 28+38+48+39+29+30=212 This proves the formula works. 8x10 Square Keystone 1 2 3 4 5 Total 42 48 54 60 66 (+6)

2. ## Number Stairs

Total for algebraic staircase= n+n+1+n+2+n+9+n+10+n+18= 6n+40 We can also evaluate that Stair number (n) = 55 By substitution stair total= 55+55+1+55+2+55+9+55+10+55+18=370 Here is another example: By substitution, stair total= 7+7+1+7+2+7+9+7+10+7+18=82 Here is another example: It is apparent that the stair number = 39 By substitution stair total= 39+39+1+39+2+39+9+39+10+39+18=274 Now that

1. ## Mathematics - Number Stairs

= 172 Algebraic Proof: n+24 n+12 n+13 n n+1 n+2 n + (n+1) + (n+2) + (n+12) + (n+13) + (n+24) = 6n + 48 8 9 10 11 12 1 2 3 T = 6n + 36 T = 6n + 40 T = 6n + 44 T =

2. ## Mathematical Coursework: 3-step stairs

3+4+5+13+14+23= 62 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58

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