Maths coursework - part two
In part two, I have been asked to investigate further into the stair totals and other step stairs on different number grids. Firstly, I will change the sizes of the stairs from 3 steps to 4, then 5, and so on to 8 step stairs. When I have finished investigating that, I will change the sizes of the grids. I will also try to find the nth term for the nth term. So I can use it to find it the nth terms of any sized step stairs, or any three step stair on any grid.
4 step stairs
Stair number = 1
Stair total = 120
31
32
33
34
21
22
23
24
1
2
3
4
2
3
4
Stair number = 2
Stair total = 130
32
33
34
354
22
23
24
25
2
3
4
5
2
3
4
5
Stair number = 3
Stair total = 140
33
34
35
36
23
24
25
26
3
4
5
6
3
4
5
6
A table to show the stair numbers
And stair totals
Stair no
2
3
Stair total
20
30
40
Finding the nth term
0 20 30
20 130 140
+10 +10 +10
0n + 110 = stair total
Checking the nth term for stair 4
0n + 110
(10 x 4) +110
40 + 110
50 = stair total for stair number 4
5 step stairs
Stair number = 1
Stair total = 235
41
42
43
44
45
31
32
33
34
35
21
22
23
24
25
1
2
3
4
5
2
3
4
5
Stair number = 2
Stair total= 250
42
43
44
45
46
32
33
34
35
36
22
23
24
25
26
2
3
4
5
6
2
3
4
5
6
Stair number = 3
Stair total = 265
In part two, I have been asked to investigate further into the stair totals and other step stairs on different number grids. Firstly, I will change the sizes of the stairs from 3 steps to 4, then 5, and so on to 8 step stairs. When I have finished investigating that, I will change the sizes of the grids. I will also try to find the nth term for the nth term. So I can use it to find it the nth terms of any sized step stairs, or any three step stair on any grid.
4 step stairs
Stair number = 1
Stair total = 120
31
32
33
34
21
22
23
24
1
2
3
4
2
3
4
Stair number = 2
Stair total = 130
32
33
34
354
22
23
24
25
2
3
4
5
2
3
4
5
Stair number = 3
Stair total = 140
33
34
35
36
23
24
25
26
3
4
5
6
3
4
5
6
A table to show the stair numbers
And stair totals
Stair no
2
3
Stair total
20
30
40
Finding the nth term
0 20 30
20 130 140
+10 +10 +10
0n + 110 = stair total
Checking the nth term for stair 4
0n + 110
(10 x 4) +110
40 + 110
50 = stair total for stair number 4
5 step stairs
Stair number = 1
Stair total = 235
41
42
43
44
45
31
32
33
34
35
21
22
23
24
25
1
2
3
4
5
2
3
4
5
Stair number = 2
Stair total= 250
42
43
44
45
46
32
33
34
35
36
22
23
24
25
26
2
3
4
5
6
2
3
4
5
6
Stair number = 3
Stair total = 265
