2. Column Sequences An Investigation

3. Column Sequences Look carefully at the columns shown below and the way in which the numbers are being put into each column. Column 1 Column 2 Column 3 Column 4 Column 5 2345 9876 10111213 17161514 18192021 25242322 26272829

4. The table continues forever in the same way as the part shown above. By looking at each column and looking at the patterns of numbers in the column see if you can answer the questions below. 1. In which column do the following numbers appear? (i) 173 (ii) 502 (iii) 1000 2. What is the 35th number in column 5? What is the 170th number in column 1. Can you find a formula to describe the numbers in each column.

5. Solution 1. (i) 173 is in column 5 (ii) 502 is in column 4 (iii)1000 is in column 2 2. 8 35-3 = 277 3. 8 170+1 = 1361 4. Column 1 sequence 9,17,25 - - - is generated by the formula u n = 8n+1, n=1, 2, 3, 4 - - - Column 2 sequence is generated by the two expressions u n = 8n-6,u n = 8n, n=1, 2, 3, 4 - - - Column 3 sequence is generated by the formula u n = 4n-1, n=1, 2, 3, 4 - - - Column 4 sequence is generated by the two expressions u n = 8n-4,u n = 8n-2, n=1, 2, 3, 4 - - - Column 5 sequence is generated by the formula u n = 8n-3, n=1, 2, 3, 4 - - -