Q1. How to use this pattern ?
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* Top row 1 : The numbers are in triangular number patterns
* At top row 1 and column x the number is x*(x+1)/2
* For example at top row 1 and column column 10 the number is 55
Q2. Find the number at row r and column c
A2. Answer
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* Number = 1 + 2 + 3 + .... (r+c-2) + c
* E.G. Number at row 1 and colum 4 is 10
* E.G. (r+c-2) = 3 Hence 1 + 2 + 3 + 4 = 10
Q3. Find row and column for number 11
A3. Answer
- At top row 1 and column x, the number is n1 = x*(x+1)/2
- The number is between two consecutive column 1 numbers
- At top row 1 and column x greater than 11 is 15
- Hence x*(x+1)/2 >= 11
- When x = 4, n1 = x*(x+1)/2 = 10
- When x = 5, n1 = x*(x+1)/2 = 15
- Hence 11 is between 10 and 15
- Hence row number is r = (15 - 11) + 1 = 5
- Hence col number is c = x - (15 - 11) = 1
Q4. Find the number at column number 9 and row number 6
- The number is
- n = 1 + 2 + 3 + .... (9 + 6 - 2) + 9
- n = 1 + 2 + 3 + .... + 13 + 9
- n = 13*(13+1)/2 + 9
- n = 13*7 + 9
- n = 100
Q5. Find the column number and row number for number 100
- The number at column x and top row 1 is n1 = x*(x+1)/2
- Where n1 is just greater than 100
- Hence x*(x+1)/2 >= 100
- When x = 12, x*(x+1)/2 = 78
- When x = 13, x*(x+1)/2 = 91
- When x = 14, x*(x+1)/2 = 105
- Hence the row number of 100 is at r = (105 - 100) + 1 = 6
- The column number is c = x - (105 - 100) = 14 - 5 = 9
Reference
- See Mathematics Dictionary Program 14 17
Now you should install Mathematics Dictionary on your computer
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(1) You can see many many diagrams for your school mathematics
(2) You can use it as graphic calculator for home work