The document provides steps to find the nth rule for a linear sequence. It uses the sequence 5, 8, 11, 14, 17 to: 1) Make a table with the terms and their position (n). 2) Find the difference between consecutive terms is 3. 3) Write this difference multiplied by n in another column. 4) The difference between this value and the term is a constant 2. 5) Therefore, the nth rule for this sequence is Term = 3n + 2.

1. 01/29/15 D. Smith 1
How to find the
nth rule for a
linear sequence

2. 01/29/15 D. Smith 2
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

3. 01/29/15 D. Smith 3
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

4. 01/29/15 D. Smith 4
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

5. 01/29/15 D. Smith 5
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

6. 01/29/15 D. Smith 6
Write the difference between the
value of 3n and the term in the
fifth column
n Term Difference 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

7. 01/29/15 D. Smith 7
The nth rule is:
Term = 3n + 2