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

An investigation into the relationship between stairs size and the value.

Extracts from this document...

Introduction

An investigation into the relationship between stairs size

...read more.

Middle

3

4

5

6

7

8

9

10

1st stair: 25 + 26 + 27 + 35 + 36 + 45 = 194

If we represent this 1st stair in the form of n then an algebraic formula can be created.

image00.png

n+(n+1)+(n+2)+(n+10)+(n+11)+(n+20)

= 6n+44

image01.png

Therefore in terms of x and y, with x being the base number and y being the total of the stair the formula would be:

y=6x+44

No matter what x is replaced by the formula (6x+44) is always applicable.

25 + 26 + 27 + 35 + 36 + 45 image07.png

= 194

(6x25) + 44 = 194

image08.png

26 + 27 + 28 + 36 + 37 + 46

= 200

(6x26) + 44 = 200

These stairs are only one along from each other on the same line.  This formula applies to any 3 levelled stairs anywhere on the grid no matter where it is.

image09.png

45 + 46 + 47 + 55 + 56 + 65

= 314

(6x45) + 44 = 314

78 + 79 + 80 + 88 + 89 + 98image10.png

= 512

(6x78) + 44 = 512

This formula however must be changed for a stair with a higher number of levels.  If the number of levels exceeds 3 then the formula (6x + 44) is incorrect.

...read more.

Conclusion

The sequence of the triangular numbers comes from the natural numbers (and zero), if you always add the next number:

1 
1+2=
3 
(1+2)+3=
6 
(1+2+3)+4=
10 
(1+2+3+4)+5=
15 
...image14.png

This diagram is identical to the number squares in the grid with the exception that they are not numbered and the diagram shows that the number of x in the formula is directly related to the number of boxes in the stair.  For example (6x+44) is the 3 level stair formula and in the diagram above there are six boxes in the 3 level stair.

The increase in x that is shown in the table shows that as the number of levels increase so does the amount of x.  The increase is by the same number.

e.g. when there are 3 levels the increase in x is by 3.  this shows that there is a sequence in the formula

...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

    if it is a 10 x 10 [10] or 11 x 11 [11] represented as algebra to give us the total of the numbers added together To start my investigation for the general formula I need to establish the highest common factors, by using our values above, which are 36,

  2. Number Grid Investigation

    n n + (w-1) n + 8(L-1) N + 8(L-1) (w-1) n x [n+8(L-1) (w-1)] = n2+ 8n (L-1)(w-1) n + (w-1) x [n + 8(L-1)] = n2 + 8n(l-1) (w-1) + 8(w-1) (L-1) Difference= 8(W-1) (L-1) The 'W' represents the length of the rectangle Whereas the 'L' represents the width.

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

    size increases by 1 then the constant number is added to the value (The highest Common Factor) In the above illustration the grid size is increasing by 1, i.e. from 10 to 11 and then to 12, using the highest common factor for 4-step grids (10)

  2. Number Stairs

    The following table shows the stair total (T) depending on the relevant stair number for the 9x9 grid. Which are from 1 to 5. N T 1 46 2 52 3 58 4 64 5 70 46 52 58 64 70 +6 +6 +6 +6 It is clear that the difference between the numbers is 6.

  1. Step-stair Investigation.

    (10*18)+(10*7)+10= 180 + 70+ 10= 260 Then added up the numbers in the 4-step stair as I did before. 18+19+20+21+25+26+27+32+33+39= 260 The two examples above prove that the formula 10x+10g+10 calculates the total of the numbers inside the area covered by a 4-step stair on any grid size.

  2. Number Stairs

    Using The formulae(6(x)+44=n) (x) Workings Total Workings (t) 35 35+36+37+45+46+55= (254) (35)+44 254 Correct 47 47+48+49+57+58+67= (326) 6(47)+44 326 Correct 58 58+59+60+68+69+78= (392) 6(58)+44 392 Correct 65 65+66+67+75+76+85= (434) 6(65)+44 434 Correct The result when using the formula 6(x)+44=(t)

  1. Number Stairs Maths Investigation

    blocks (for example, on a 3 by 3 number grid the block in the top right hand corner will be 3w and on a 8 by 8 number grid the block in the top right hand corner will be 8w). Upon elaboration of the number grid on Page 2 (Fig.

  2. 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 =

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