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• Level: GCSE
• Subject: Maths
• Word count: 1054

# Number Stairs investigation.

Extracts from this document...

Introduction

Number Stairs investigation

The task of this coursework is to investigate the relationship between the total of a 3-step stair and the position of it on a 10 x 10 grid.

The three step stair is made up of 6 squares.

X = Stair number or Sn

I will carry out the investigation in the following steps:

- On a 10 x 10 grid move the ‘stairs’ 1 square to the right and find the stair total, by adding all the numbers in the stair together.

- Put the information into a table and look for any pattern or rules.

- Describe any patterns or rules using words and/or algebra.

- Try to explain any patterns found.

-

Middle

6                                80                                                6

7                                86                                                6

Each time the stair total increases by 6.  This takes the previous total to the next total.

To get the formula I multiplied each stair total by 6.  I noticed that after each multiplication the only difference between the number and the ST was 44.

Therefore the formula is Dn+(A-D)

6n+(50-6)

6n+44

The stair number is multiplied by 6 and 44 is added to make the stair total.

The formula allows the stair total to be obtained from only the star number.

Part 2

As said in my plan I intend to try different step sizes on the same 10 x 10 grid.  I will try a 2-step stair.

From my previous investigation I figured that

Conclusion

The total of the difference is 20 + 10 + 11+ 1 +2 = 44

The difference when added together makes the number that must be added at the end of the formula (i.e.6n + 44).

I will see if this applies to all stair sizes.

 11 1 2 Sn+10 Sn Sn+1

The total of the differences is 11.  This is also the end of the rule(3n + 11).

 41 31 23 21 22 23 11 12 13 14 1 2 3 4 5
 Sn+40 Sn+30 Sn+31 Sn+20 Sn+21 Sn+22 Sn+10 Sn+11 Sn+12 Sn+13 SN Sn+1 Sn+2 Sn+3 Sn+4

Total difference = 220

Formula = 15n +220

The rule for finding the differences works.

I will try to find the rules for larger stair numbers.

 51 41 42 31 32 33 21 22 23 24 11 12 13 14 15 1 2 3 4 5 6
 Sn+50 Sn+40 Sn+41 Sn+30 Sn+31 Sn+32 Sn+20 Sn+21 Sn+22 Sn+23 Sn+10 Sn+11 Sn+12 Sn+13 Sn+14 SN Sn+1 Sn+2 Sn+3 Sn+4 Sn+5

As there are 21 squares I will say the start of the rules is 21n.  The total of the differences is 385.  The formula can is 21n + 385.

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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