Mathematics coursework- explaining the relationship of the 3-step stair

GSCE COURSEWORK PART 1 Random Sample I drew 5 3-step stairs all of them were the same size, but they differed in position. Comment: 1) Notice how all the totals are even 2) The totals increase the higher up the grid you go 3) Across goes up about 42 (92-50) 4) Up goes up about 420 (470-50) Systematic Sample I drew 5 stairs all on the bottom line going across, I did this to see if there was a pattern. Comment: There is clearly …showed first 75 words of 1147 total…

…showed last 75 words of 1147 total…works for the 3-step stairs. I will do the same, but this time for a 7 step stairs: [7(7+1)]/2 x + [7(7+1) (7-1)]/6 g + [7(7+1) (7-1)]/6 which equals: 28x+56g+56 Clearly my formula works, through the use of algebra and my insight into the relationships of series and triangle numbers I was able to achieve this. I needed to use a variety of methods and techniques to complete the universal formula, always linking it back with previous formulas and tables.