Find number at row 7 and column 7
Q1. How to use this pattern ?
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* Left Column 1 : The numbers in triangular number patterns
* At column 1 and row x the number is x*(x+1)/2
* For example at column1 1 row 10 the number is 55
Q2. Find the number at row r and colum c
A2. Answer
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* Number = 1 + 2 + 3 + .... (r+c-2) + r
* E.G. Number at row 4 and left column 1 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 left column 1 and row x, the number is n1 = x*(x+1)/2
- The number is between two consecutive numbers in left column 1
- At left column 1 and row x is 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 col number is c = (15 - 11) + 1 = 5
- Hence row number is r = x - (15 - 11) = 1
Q4. Find the number at column number 3 and row number 6
- The number is
- n = 1 + 2 + 3 + .... (3 + 6 - 2) + 6
- n = 1 + 2 + 3 + .... + 7 + 6
- n = 7*(7+1)/2 + 6
- n = 7*4 + 6
- n = 34
Q5. Find the column number and row number for number 34
- The number at column 1 and row x is n1 = x*(x+1)/2
- Where n1 is just greater than 34
- Hence x*(x+1)/2 >= 34
- When x = 6, x*(x+1)/2 = 21
- When x = 7, x*(x+1)/2 = 28
- When x = 8, x*(x+1)/2 = 36
- Hence the column number of 34 is at c = (36 - 34) + 1 = 3
- The row number is r = x - (36 - 34) = 8 - 2 = 6
Reference
- See Mathematics Dictionary Program 14 17
Reference (1) : Coordinate geometry in analytic geometry
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Algebra
AL 08 05