1. Column Sequences
An Investigation

2. Column Sequences Column 1 Column 2 Column 3 Column 4 Column 5 2 3 4 5
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 2 3 4 5 9 8 7 6 10 11 12 13 17 16 15 14 18 19 20 21 25 24 23 22 26 27 28 29

3. 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) (ii) (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.

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