1. Sequences That was easy
A sequence is an ordered list of numbers that often form a pattern.
Each number in the list is called a term of the sequence.
A wooden post-and-rail fence is made as shown below. How many pieces of wood are needed to build a 4-section fence, a five-section fence, a six-section fence?
I think I see a pattern.
1 section
4 pieces
2 sections
7 pieces
3 sections
10 pieces
6-section fence
+ 3
+ 3
4-section fence
19 pieces
5-section fence
13 pieces
That was easy
16 pieces

2. Extending Sequences That was easy Describe a pattern in each sequence.
Determine what the next two terms are.
5, 8, 11, 14,…
17, 20
2, -4, 8, ,…
32,
+ 3
+ 3
+ 3
* -2
* -2
* -2
3, 6, 12, 24,…
48, 96
8, 3, -2, -7,…
-12,
* 2
* 2
* 2
- 5
- 5
- 5
400, , , 50,…
25,
* ½
* ½
* ½
That was easy

3. Arithmetic Sequences Asi De Facil
In an arithmetic sequence the difference between consecutive terms is constant.
An arithmetic sequence follows a pattern of adding a fixed amount from one term to the next.
This difference is called the common difference.
3, 8, 13, 18,…
9, 2, -5, ,…
5, 9, 12, 14,…
+ 5
+ 5
+ 5
- 7
- 7
- 7
+ 4
+ 3
+ 2
There is a common difference of 5, so it is arithmetic.
There is a common difference of -7, so it is arithmetic.
There is no common difference, so it is not arithmetic.
2, 6, 18, 54,…
That’s not a common difference.
That’s not adding. *3 *3 *3
There is no common difference derived by addition, so it is not arithmetic.
Asi De Facil

4. Identifying Arithmetic Sequences
Tell whether the sequence is arithmetic.
If it is, what is the common difference?
8, 15, 22, 30,…
0.2, , , ,…
7, 9, 11, 13,…
+ 7
+ 7
+ 8
+ 1.3
+ 1.3
+ 2
+ 2
+ 2
+ 1.3 No
Yes
CD = + 1.3
Yes
CD = +2
10, 4, -2, -8,…
2, -2, 2, -2,…
2, 11, 21, 32,… -6 -6 -6
* -1
* -1
* -1
+ 9
+ 10
+ 11
Yes
CD = -6 No No

5. Practice with Sequences
a) Describe a pattern in each sequence.
b) Determine what the next two terms are.
c) Explain why the sequence is or is not arithmetic.
7, 3, -1, -5,…
2, 4, 8, 16,…
- 4
- 4
- 4
* 2
* 2
* 2
a) Add negative 4
c) It is arithmetic because the common difference is 4 and the pattern is addition.
a) Multiply by 2
c) It is not arithmetic because there is not a common difference derived by addition.
b) -9, -13
b) 32, 64
1, -3, 9, ,…
12, 19, 26, 33,…
* -3
* -3
* -3 +7 +7 +7
a) Multiply by negative 3
c) It is not arithmetic because there is not a common difference derived by addition.
a) Add 7
c) It is arithmetic because the common difference is 7 and the pattern is addition.
b) 40, 47
b) 81, -243

6. Homework
Page 279: 10 – 28
Even Numbers

7. Recursive Formula
A recursive formula is a function rule that relates each term of a sequence after the first term to the ones before it.
3, 11, 19, 27,…
Let n = the term number in the sequence
Let A(n) = the value of the nth term in the sequence
CD = +8
Value of term 1 =
A(1) = 3
The recursive formula for this sequence is
Value of term 2 =
A(2) =
A(1) + 8 =
3 + 8 = 11
Value of term 3 =
A(3) =
A(2) + 8 = = 19
Value of term 4 =
A(4) =
A(3) + 8 = = 27
Value of term n =
A(n) =
A(n - 1) + 8

8. Writing a Recursive Formula
Write a recursive formula for the given sequence
23, 35, 47, 59,…
97, 88, 79, 70,…
That was easy
CD = +12
CD = -9
A(1) = 23
A(1) = 97
A(2) =
A(1) + 12 = = 35
A(2) =
A(1) - 9 = = 88
A(3) =
A(2) + 12 = = 47
A(3) =
A(2) - 9 = = 79
A(4) =
A(3) + 12 = = 59
A(4) =
A(3) - 9 = = 70
A(n) =
A(n - 1) + 12
A(n) =
A(n - 1) - 9

9. More Writing Recursive Formulas
Write a recursive formula for the given sequence
70, 77, 84, 91,…
4.6, , , ,…
CD = +7
CD = +0.1
Asi De Facil
13, 10, 7, 4,…
13, 5, -3, ,…
CD = -3
CD = -8

10. Explicit Formula 16, 27, 38, 49,… CD = +11
An explicit formula is a function rule that relates each term of a sequence to the term number
nth term
first term
term number
common difference
16, 27, 38, 49,…
CD = +11

11. Writing an Explicit Formula from a Recursive Formula

12. Homework
Page 279:
Even Numbers

13. Writing an Recursive Formula from a Explicit Formula
first term
term number
common difference

14. More Writing an Recursive Formula from a Explicit Formula
That was easy

15. Finding Specific Terms with an Explicit Formula
Find the third, fifth, and thirteenth terms of the sequence described by each explicit formula.

16. More Finding Specific Terms with an Explicit Formula
Find the third, fifth, and thirteenth terms of the sequence described by each explicit formula.

17. Homework
Page :
Even Numbers