Linear sequences A linear sequence is a name for a list of numbers where the next number is found by adding or subtracting a constant number. Here is an example: 31/12/2018 D. Smith

5, 8, +3 31/12/2018 D. Smith

5, 8, 11, +3 +3 31/12/2018 D. Smith

5, 8, 11, 14 +3 +3 +3 31/12/2018 D. Smith

5, 8, 11, 14, 17… etc +3 +3 +3 +3 31/12/2018 D. Smith

1 2 3 4 5 8 11 14 17 Finding the a rule for the nth term Position (n) This is a rule that connects a term’s position (n) with its value. Position (n) 1 2 3 4 5 Value 8 11 14 17 31/12/2018 D. Smith

Find the nth rule for this sequence: 5, 8, 11, 14, 17… Make a table with 5 columns and write the position of the terms – 1st 2nd 3rd 4th etc as the n numbers in the first column n 1 2 3 4 5 31/12/2018 D. Smith

Put the terms into the second column, 5, 8, 11, 14, 17… 2 8 3 11 4 14 17 6 31/12/2018 D. Smith

Find the difference between the terms 8 – 5 = 3 and write it in the third column 1 5 3 2 8 11 4 14 17 6 31/12/2018 D. Smith

Write the difference number multiplied by the n number in the fourth column Term Difference 3n 1 5 3 2 8 6 11 9 4 14 12 17 15 31/12/2018 D. Smith

Write the difference between the value of 3n and the term in the fifth column Term – 3n 1 5 3 2 8 6 11 9 4 14 12 17 15 31/12/2018 D. Smith

The nth rule is: Term = 3n + 2 31/12/2018 D. Smith

n Term = 3n + 2 Term 1 3 X 1 + 2 5 2 3 X 2 + 2 8 3 3 X 3 + 2 11 4 3 X 4 + 2 14 3 X 5 + 2 17 31/12/2018 D. Smith