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• Level: GCSE
• Subject: Maths
• Word count: 1559

# 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.

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Introduction

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 11 12 13 14 1 2 3 4 Stair number = 2 Stair total = 130 32 33 34 354 22 23 24 25 12 13 14 15 2 3 4 5 Stair number = 3 Stair total = 140 33 34 35 36 23 24 25 26 13 14 15 16 3 4 5 6 A table to show the stair numbers And stair totals Stair no 1 2 3 Stair total 120 130 140 Finding the nth term 10 20 30 120 130 140 +10 +10 +10 10n + 110 = stair total Checking the nth term for stair 4 10n + 110 (10 x 4) ...read more.

Middle

4 5 6 7 8 Stair number = 3 Stair total = 700 63 646566 65 66 67 68 69 53 54 55 56 57 58 59 43 44 45 46 47 48 49 33 34 35 36 37 38 39 23 24 25 26 27 28 29 13 14 15 16 17 18 19 3 4 5 6 7 8 9 A table to show the stair numbers and Their stair totals Stair number 1 2 3 Stair total 644 672 700 Finding the nth term 28 56 94 644 672 700 +28 +28 +28 28n + 616 Checking the nth term for stair 4 28n + 616 (28 x 4)+ 616 = 728 = stair total for stair 4 8 step stairs Stair number = 1 Stair total = 960 71 72 73 74 75 76 78 79 61 62 63 64 65 66 67 68 51 52 53 54 55 56 57 58 41 42 43 44 45 46 47 48 31 32 33 34 35 36 377 38 21 22 23 24 25 26 27 28 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 Stair number = 2 Stair total = 996 72 73 74 75 76 77 78 79 62 63 64 65 66 67 68 69 52 ...read more.

Conclusion

+ 32 56 = stair total for stair 4 8 x 8 grid Stair number = 1 Stair total = 42 17 18 19 9 10 11 1 2 3 Stair number = 2 Stair total = 48 18 19 20 10 11 12 2 3 4 Stair number = 3 Stair total = 54 19 20 21 11 12 13 3 4 5 Stair no 1 2 3 Stair total 42 48 54 Nth term 6 12 18 42 48 54 +6 +6 +6 6n + 36 Check nth term for stair 4 6n + 36 (6 x 4) + 36 60 = stair total for stair 4 Nth term of nth term 6n + 28 +4 6n + 32 +4 6n + 36 +4 4 8 12 28 32 36 +4 +4 +4 4n + 24 Then with the answer, put 6n + in front of it. Check nth term for fourth nth term (9 x 9) grid 4n + 24 (4 x 4) +24 40 = 6n + 40 = nth term for step stair on 9 x 9 grid. After all of my investigating, I have come up with a formula to find out the nth term of any three step stair on any grid. I have also found out how to find the stair totals of any three step stair on a 10 x 10 grid. ?? ?? ?? ?? ...read more.

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