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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.

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