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T-Total Investigation

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Introduction

Maths Coursework – T-Total

I have looked at the T-Number and I called it N. Then I saw how much difference there was between the T-Number and the other numbers in the T. when I did this the numbers came out like this:        20, 20-9, 20-19, 20-18, 20-17. These sums when added together will come out with the T-Total. The T-Total is 37. I have tried out this method with other T-Numbers and the results ended up like this.

T-Number                T-Total

  1. 37
  2. 42
  3. 47
  4. 52
  5. 57
  6. 62
  7. 67
  8. 72
  9. 77
  10. 82

This rule showed a pattern. The next T-Total has 5 added to it. This means that there has to be a 5 in the algebraic rule. Because there are 5 squares in a T the 5 in the rule will be 5N. 5N for the first T-Number is 100. To get to the proven T-Total for this T-Number I have to minus 63. So the rule for this T-Number is 5N – 63. I will now test whether this rule works for the other

T-Numbers.

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Middle

22, 22-10, 22-20, 20-21, 20-19. This ends up minusing 70 from the 5N.The final T-Total now is 40. I will now try this for other T-Numbers. 5 times 25 is 125, then minus 70 is 55. I tested this and it is correct. 5 times 26 is 130 then minus 70 is 60. This is correct aswell.

The Nth Term for finding out the T-Total on a 10x10 grid is 5N – 70.

I will now try on an 8x8 grid. I will start off with the T-Number 30. 30 times 5 is 150. Now I will do the same as before to get the T-Total. 30, 30-8, 30-16, 30-17, 30-15. Now I have to minus 56. This comes out with 94. I added up the numbers and they do equal 94. I tried this for other T-Numbers and it worked.

The Nth Term for finding out the T-Total on an 8x8 grid is 5N – 56.

I have looked at all of the Nth Terms and I can see a pattern. The number needed to minus to get the T-Total is related to the grid size. The grid size times 7 equals the number. 7x8=56. 7x9=63. 7x10=70.

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Conclusion

The Nth Term for the T on its side facing left on a 9x9 grid is 5N + 7.

I will now try it on a 10x10 grid facing right with the T-Number 13. 13, 13-1, 13-2, 13-12, 13+8. It is again 5N – 7. So I predict that it will be the opposite for the facing left. I will test it with the T-Number 15. 15, 15+1, 15+2, 15+12, 15-8. It does come out as 5N + 7.  Because the rule is the same for the grid sizes 9x9 and 10x10 grid that it will be the same again for the grid size 8x8. I will now test it with the T facing left with the T-Number 9. 9, 9+1, 9+2, 9-6, 9+10. This adds up to 5N + 7. Now I will try it facing right with the T-Number 11. 11, 11-1, 11-2, 11+6, 11-10. I adds up to 5N – 7 again.

The overall Nth Term for the T on its side facing left on is 5N + 7.

The overall Nth Term for the T on its side facing right on is 5N - 7.

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