Column Sequences

An Investigation

Column SequencesLook 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

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.

Solution1. (i) 173 is in column 5 (ii) 502 is in column 4 (iii)1000 is in column 22. 8 35-3 = 2773. 8 170+1 = 1361 4. Column 1 sequence 9,17,25 - - - is generated by

the formula un= 8n+1 , n=1, 2, 3, 4 - - -Column 2 sequence is generated by the two expressions

un= 8n-6 ,un= 8n, n=1, 2, 3, 4 - - -Column 3 sequence is generated by

the formula un= 4n-1 , n=1, 2, 3, 4 - - -Column 4 sequence is generated by the two expressions

un= 8n-4 ,un= 8n-2, n=1, 2, 3, 4 - - -Column 5 sequence is generated by

the formula un= 8n-3 , n=1, 2, 3, 4 - - -