I drew 5 3-step stairs all of them were the same size, but they differed in position.
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)
I drew 5 stairs all on the bottom line going across, I did this to see if there was a pattern.
There is clearly a pattern here; the totals are increasing by 6, we call this a linear sequence.
From this information I predict that the next total will be 80 and the 8th will be 92.
Both my predictions were correct.
I drew 1 stair with Algebra on it.
(x)+(x+1) +(x+2) +(x+10) +(x+11) +(x+20) = 6X+44
The reason it's 6x is because there are 6 stairs (x+x+x+x+x+x)
It's 44 because the totals across for these stairs are 4 across and 40 upwards.
1: This 1 came from the 11, because you go 1 across from the 10 to get 11
10: This 10 came from the 11, because you go 10 up from the 1 to get 11
I have changed the grids to see whether or not there is a pattern. I kept the shape name as one all the time. I have done 5, 6,7and 8 grids.
There is clearly a pattern here; the totals are increasing by 4; so each time I increase the grid size by 1 the total increases by 4, there is a common difference.
From this information I predict that the 9th grid will have a total of 46.
My prediction was correct.
I have drawn a 3-step stair...