number stairs

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Nazma Khan 10A

Maths coursework

Number Stairs

In this coursework, I will be investigating the relationship between the stair totals and the position of the stair shape on the grid. I will be using the 3 step stair on a 10 by 10 grid to find out a relationship, which will help me to solve any problem regarding to solve the 3 step stair. The 10 by 10 grid is order in the reverse order from 1-100, starting from 1 situated at the bottom left hand corner and the 100 at the top right hand corner. However in order to see a sequence I would be carrying out this investigation in a systematic order in order to see a pattern. The way in which I will be systematic is by starting from the smallest number and the moving 1 box to the right each time.

This is how the grid looks like on a 10 by 10 grid and also how the 3 step stair looks like:

Therefore in order for me to see a pattern occurring, I will be moving this 3 step stair, systematically to find out a formula for the total of the three step stair, which works for the entire 3 step stair on a 10 by 10 grid. The way in which I will be approaching this method is shown below:

        

                                        14+15+16+24+25+34= 128

         15+16+17+25+26+35= 134

        

        16+17+18+26+27+36= 140

        17+18+19+27+28+37= 146

As you can see I have moved the step stair systematically 1 step towards the right, and also I first started off with the smallest number first, in order to see a pattern emerging.

Therefore the difference is 6. So you multiply 6 x 14 =84

Then to get the answer 128 you + 44.              84 + 44= 128

Furthermore I will be extending my investigation further by changing the size of steps, e.g. 1 step stair, 2 step stair…, on a 10 by 10 grid. I believe that as a result to this it will allow me to see a link between the stair total, therefore I will be trying to get an overall formula which will work for the entire step stair on a 10 by 10 grid.

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I will be using the same method but in algebra form.

        χ        

        χ+χ+1+χ+10 = 3χ + 11

                             χ+χ+1+χ+2+χ+10+χ+11+χ+20= 6χ+44

                 χ+χ+1+χ+2+χ+3+χ+10+χ+11+χ+12+χ+20+χ+21+χ+30 =10χ+110

        15χ+1+2+3+4+10+11+12+13+20+21+22+30+31+40=

                                                   

              ...

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