The document outlines a lesson on finding the nth term of arithmetic sequences. By the end of the lesson, all students should be able to determine the rule for a sequence using n, most should be able to find the nth term, and some should be able to write a sequence given the rule in terms of n. The lesson provides examples of finding the rule for sequences where terms increase or decrease by a common amount. It explains that the rule can be written in terms of n and how knowing the rule allows students to find specific terms like the 100th term.

1. 9th February 2012
Objective: to be able to find the nth term of an
arithmetic sequence. (Grade D)
Skills: Absorption and Making Links
By the end of the lesson:
All: work out the rule for a sequence (with n)
Most: will be able to find the nth term of sequence
Some: will be able to write a sequence from the rule in
terms of n

3. Starter
State the rule for the following sequences
1.
2.
3.
4.
5.
16, 26, 36, 46, 56, ...
8, 11, 14, 17, 20, ...
9, 11, 13, 15, 17, ...
0, 4, 8, 12, 16, ...
-1, 4, 9, 14, 19, ...

4. From the previous lesson
What were the 2 things we looked for when
finding the rule for a sequence?
1. The amount each goes up by
2. What we needed to add or subtract to get
our first term.

5. nth term
Look at the following sequence
7, 13, 19, 25, 31, ....
What is the rule?
x6 + 1
So we can write this as
6n + 1

6. nth term
Look at the following sequence
3, 7, 11, 15, 19, ....
What is the rule?
x4 – 1
So we can write this as
4n – 1

7. nth term
Look at the following sequence
11, 21, 31, 41, 51, ....
What is the rule?
x10 + 1
So we can write this as
10n + 1

8. How can we find the rule?
Look at the sequence:
Look at the sequence:
4, 7, 10, 13, 16
2, 6, 10, 14, 18
What is the rule in terms
of n
3n + 1
What is the rule in terms
of n
4n-2

9. Find the rule in terms of n.....
• Green
1. 2, 5, 8, 11, 14
2. 4, 8, 12, 16, 20
3. 9, 11, 13, 15, 17
4. 2, 6, 10, 14, 18
5. 4, 10, 16, 22, 28
Extension
3, -2, -7, -12, ...
• Red
1. 0, 4, 8, 12, 16
2. 1, 6, 11, 16, 21
3. 2, 8, 14, 20, 26
4. 9, 17, 25, 33, 41
5. -4, 2, 8, 14, 20

10. Answers
• Green
1. 3n-1
2. 4n
3. 2n+7
4. 4n-2
5. 6n-2
Extension
-5n + 8
• Red
1. 4n-4
2. 5n-4
3. 6n-4
4. 8n+1
5. 6n - 10

11. What about when the sequence goes
down...
What is the nth term of this sequence
2, 0, -2, -4, ...
0, -3, -6,-9, ...

12. Find the rule in terms of n.....
• Green
• Red
1)
2)
3)
4)
5)
1)
2)
3)
4)
5)
-2, -5, -8, -11, ...
4, 1, -2, -5, ...
8, 4, 0, -4, -8, ...
2, -3, -8, -13, ...
10, 6, 2, -2, ....
-3, -7, -11, -15,...
1, -3, -7, -11, ...
24, 12, 0, -12, ...
6, 1, -4, -9, ...
4, -3, -10, -17, ...

13. Answers
• Green
1. -3n + 1
2. -3n + 7
3. -4n + 12
4. -5n + 7
5. -4n + 14
• Red
1. -4n + 1
2. -4n + 5
3. -12n + 36
4. -5n + 11
5. -7n + 11

14. How does this help us?
• If I know a sequence has a rule 3n how could i
find the 100th term?
• If i know a sequence has a rule 5n - 3 how
could I find the 100th term?

15. Questions
• Green
If I have the sequence
3n find the
1. 1st term
2. 4th term
3. 10th term
4. 100th term
• Red
If I have the sequence
5n – 2 find the
1. 1st term
2. 5th term
3. 20th term
4. 100th term
5. 1000th term

16. To finish
• Someone has missed the lesson. You have to
send them a text about what you learned in
this lesson. Use 160 characters (a text
message) to tell them what you learned today