Linera sequence
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This document provides an example of finding the rule for a linear sequence, where each term is found by adding a constant to the previous term. It shows working through an example sequence where the terms are 5, 8, 11, 14, 17 etc and each term is 3 greater than the previous term. It demonstrates setting up a table with the term position (n) and values, finding the difference between terms, and the rule that the nth term is given by the expression Term = 3n + 2.
Linera sequence
- 1. 01/28/15 D. Smith 1 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:
- 2. 01/28/15 D. Smith 2 5, 8, +3
- 3. 01/28/15 D. Smith 3 5, 8, 11, +3 +3
- 4. 01/28/15 D. Smith 4 5, 8, 11, 14 +3 +3 +3
- 5. 01/28/15 D. Smith 5 5, 8, 11, 14, 17… +3 +3 +3 +3 etc
- 6. 01/28/15 D. Smith 6 Finding the a rule for the nth term Position (n) 1 2 3 4 5 Value 5 8 11 14 17 This is a rule that connects a term’s position (n) with its value.
- 7. 01/28/15 D. Smith 7 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
- 8. 01/28/15 D. Smith 8 Put the terms into the second column, 5, 8, 11, 14, 17… n Term 1 5 2 8 3 11 4 14 5 17 6
- 9. 01/28/15 D. Smith 9 Find the difference between the terms 8 – 5 = 3 and write it in the third column n Term Difference 1 5 3 2 8 3 3 11 3 4 14 3 5 17 3 6
- 10. 01/28/15 D. Smith 10 Write the difference number multiplied by the n number in the fourth column n Term Difference 3n 1 5 3 3 2 8 3 6 3 11 3 9 4 14 3 12 5 17 3 15 6
- 11. 01/28/15 D. Smith 11 Write the difference between the value of 3n and the term in the fifth column n Term Difference 3n Term – 3n 1 5 3 3 2 2 8 3 6 2 3 11 3 9 2 4 14 3 12 2 5 17 3 15 2 6
- 12. 01/28/15 D. Smith 12 The nth rule is: Term = 3n + 2
- 13. 01/28/15 D. Smith 13 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 5 3 X 5 + 2 17