• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Number Stairs

Extracts from this document...

Introduction

GCSE Coursework – Number Stairs Investigation

Part 1

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

59

60

41

42

43

44

45

46

47

48

49

50

31

32

33

34

35

36

37

38

39

40

21

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

image00.png

This is a 10 x 10 size grid with a 3-stair shape in gray. This is called the stair total.

  The stair total for this stair shape is 25 + 26 + 27 + 35 + 36 + 45 = 194.

 To investigate the relationship between the stair total and the position of the stair shape, I will use the far-left bottom square as my stair number:

This is always the smallest number in the stair shape. It is 25 for this stair shape.

 Now , I'm going to translate this 3-stair shape to different positions around the 10 x 10 grid:

44

34

35

24

25

26

...read more.

Middle

The stair-total for this stair shape is   4 + 5 + 6 + 14 + 15 + 23 = 68

 This table summarizes these results :

Stair number

24

25

26

25

3

4

Stair Total

188

194

200

206

62

68

  In order to find a formula which give  the stair total when I am given the stair number,

  I am going to put the stair number as the position and the stair total as the term for the

   sequence:

Position

24

25

26

27

3

4

Term

188

194

200

206

62

68

Difference

+6

+6

+6

  I have noticed that there is an increase of 6 between two consecutive terms in this

  arithmetic sequence. Therefore the term rule must be  6 x Position±  number .

Position (n)

24

25

26

27

3

4

Term ( T )

188

194

200

204

62

68

    6n

144

150

156

162

18

24

+  or  

+44

+44

+44

+44

+44

+44

   We can notice that the term is always 6 times the position, Add 44 .

...read more.

Conclusion

To check if this formula works for other stair numbers, I will try another numbe 55

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

59

60

41

42

43

44

45

46

47

48

49

50

31

32

33

34

35

36

37

38

39

40

21

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

Stair-total =         6n + 44

( using the formula )  = 6(55) + 44

                                    = 330 + 44

                                =  374

Stair-total         = 55 + 56 + 57 + 65 +  66 + 75

( by adding )        =         374

This shows that my formula must work for all stair-numbers in 3-stair shapes on the 10 x 10 grid.

 However, I have observed that you could just sub any number as 'n' into the formula and

 you could still get a stair total even if that stair shape cannot actually be drawn on the grid.

 For instance, we could  substitute  'n'  by 10 into the formula like this:

 Tn = 6n + 44

       = 6(10) + 44

       = 60 + 44

       = 104

  However it is impossible to draw a stair shape with the bottom left-hand number as

  10, simply because it would not fit.

...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.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Number stairs

    a 3-stepped, 4-stepped, or 5-stepped etc or where its position is in a numbered grid, such as 10x10, or 23x23 etc the general formula will always give the total of the grid numbers in that step stair.

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

    shown below: Table 13 a 32x32 and 45x45 grid: 1 1 33 34 46 47 65 66 67 91 92 93 Using our equation we use the [x] and [n] values we see the results below: (6 x 65) - (4 x (32 - 1)

  1. Number Stairs

    + 36= 282 Stair number=27 Whereas stair total= 27+28+29+35+36+43=198 But by using the nth term, stair total= (6x27) + 36= 198 Here is an alternative way to find the stair total of the 8x8 grid by using further algebraic method.

  2. Mathematical Coursework: 3-step stairs

    Nonetheless, I will use different shaped grids i.e. 6cm by 6cm to demonstrate that my formula is utilize in any circumstance. In addition, I will change the 3 step stairs into different steps such as; 4-step stairs. These changes enable me to investigate further and fully grasp the perception of the link between the stair shape and stair total.

  1. number grid investigation]

    of the box using a formula that remains constant: Formula 3: Bottom Left (BL) = (Width (w) - 1) x 10 The formulas stated above can be used to calculate these terms in any given table: TL: n ~ TR: Formula 2 ~ ~ ~ BL: Formula 3 ~ BR:

  2. Maths Number Stairs

    (4)1/2 10n + 110 = t = 8 + 2 = 10 I am correct 10 is the triangular number. Finding the formula 3n 6n --> For this half I have found part of my general 10n formula. I will now look at the patterns and find 15n a formula for the other side.

  1. Number stairsMy aim is to investigate the relationship between the stair total and the ...

    stairs by taking all the 4 step stairs on the bottom row and finding the sum. 1)1+2+3+4+11+12+13+21+22+31=120 2)2+3+4+5+12+13+14+22+23+32=130 3)3+4+5+6+13+14+15+23+24+33=140 4)4+5+6+7+14+15+16+24+25+34=150 5)5+6+7+8+15+16+17+25+26+35=160 6)6+7+8+9+16+17+18+26+27+36=170 7)7+8+9+10+17+18+19+27+28+37=180 Using the formula Un=ab+c I can tell that the terms go up in tens. This tells me that the nth term will include 10 lots of n or 10n.

  2. Maths Coursework: Number Stairs

    I can therefore conclude that the general equation for a 3-step stair on a 10 by 10 number grid is 6n + 40 = stair total where n is the base number. (Shaded box). Total of step containing 1 as its base number - Difference = 50 - 6 =

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work