• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2

# maths stairs

Extracts from this document...

Introduction

Luke Griffiths

Number Stairs part 2

I am going to be investigating the relationship between stair totals using 3 by 3 size step stairs on different size grids. I am looking for an equation that will link the stair total to the size of the grid. I am going to do 3 different grid sizes and then predict the 4th. If I am successful I will use the formula. If I am unsuccessful I shall try again. I will use 1 as the corner squares, testing on 2, n as the term for the corner square, and g as the grid size. How I got the formula is explained in part 1. (Diagrams are above)

I

Middle

I have worked out that if the corner square is 1 in a 4 by 4 grid the total will be.

1+2+3+5+6+9=26

I worked this out by adding all of the numbers inside the stair and finding the total.

I came up with the formula of 20+6n. As there is still the same number of ‘n’ in the diagram, the only change is that of the numbers. To test this I will do both on the

I predict that if the corner square is 2 in a 4 by 4 grid the total will be.

(6*2)+20=32

To prove I used the other method as well.

2+3+4+6+7+10=32

Therefore the 4 by 4 grid formula for a 3 step stair is 6n+20.

I have now moved on to a 5 by 5 grid.

Conclusion

span class="c3">However to prove this I predict that for the next grid increase, 6 by 6, the formula will be 6n+28.

Which would therefore mean that the formula would be (6*1)+28=34

1+2+3+7+8+13=34

Therefore this constant increase is apparent and therefore I can use this to draw up a table of results, which is shown below.

Now I need a general formula for a 3 step stair on any grid size. I will use g to represent the grid size.

The diagram is following. I have seen that the grid size is also the amount the n increases by from line to line. Therefore n+g will be the correct number proved by:

n=1, g=3

n+g=4

4 is the number directly above n so therefore is n+g therefore the formula is correct.

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

# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Number stairs

relationship between the stair totals and other step stairs on other number grids. Using my algebra equations and my proven theory for 3-step, I am going to use the same approach and theory as I used in the 3-step exercise, I can apply the same to the 4-step stair to

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

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

1. ## Number Stairs

27 19 20 11 12 13 3 4 5 6 Here we can see that stair number = 2 Stair number = 3 Whereas, stair total = 2+3+4+5+10+11 Stair total = 3+4+5+6+11+12+13+19+20+27=120 +12+18+19+26= 110 The following table shows the stair total (T)

2. ## GCSE Maths Sequences Coursework

Total Total is equal to Shaded plus Unshaded so; 3N + 1.5N�-1.5N+1 1.5N�+1.5N+1 Nth term for Total = 1.5N�+1.5N+1 I have now found that my general formulae are correct as I used them to predict the shaded, unshaded and total for triangles and have found that my predictions are correct.

1. ## Maths coursework. For my extension piece I decided to investigate stairs that ascend along ...

+ (n + g + 4) + (n + 2g) + (n + 2g + 1) + (n + 2g + 2) + (n + 2g + 3) + (n + 3g) + (n + 3g + 1) + (n + 3g + 2) + (n + 4g)

2. ## Maths Coursework: Number Stairs

by 11 = 6x + 48 So from the results table I can see a linear pattern, which confirms my theory. Every time you increase the grid size by 1 you increase the formula by 4 Here is the diagram that illustrates the equation for any 3-step stair on any

1. ## Mathematics - Number Stairs

21 + 31 = 72 Algebraic Proof: n+11 n n+1 n + (n+1) + (n+11) = 3n + 12 8 9 10 11 12 1 2 T = 3n + 9 T = 3n + 10 T = 3n + 11 T = 3n + 12 3 T = 6n

2. ## Number Stairs

So I know the formula have something to do with (6) Multiplied by Bottom left corner of the stair (x), Added or Subtracted by number (n), is equal to Total Stair Total (t). 6x +/- n=t If 'x' = 1, then 't' = 50.

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