Teacher:________________
Room: _________________
Sequence (Notes)
Vocabulary:
1. Sequence – A series of numbers that follow a pattern
2. Term – Individual number in a sequence
3. Arithmetic Sequence – Consecutive terms are formed by adding or subtracting the same
number (common difference)
4. Geometric Sequence – Consecutive terms are formed by multiplying or dividing by the
same factor (common multiplier or ratio)
5. n – The numerical position or location of a term in a sequence, always start with 1.
Examples:
Position
Term
Rule
Position
Term
Rule
1
4
2
6
+2
1
9
3
8
+2
2
18
x2
+2
3
36
x2
1
2
3
1/9 1/3
1
x3
x3
Position
Term
Rule
1
15
2
17
4
72
6
288
x2
5
9
x3
4
24
+4
+2
x2
x3
6
14
5
144
4
3
3
20
+3
5
12
+2
x2
Position
Term
Rule
+2
4
10
6
27
x3
5
29
+5
Arithmetic
sequence
Geometric
Sequence
Geometric
Sequence
6
35
+6
Neither
Exercise:
Prentice Hall Practice 11- 1 p 411
1
Writing Algebraic Expression on Arithmetic sequence (Notes)
Position
Term
Rule
1
4
+2
2
6
+2
3
8
+2
4
10
+2
5
12
+2
6
14
n
+2
. According to the pattern, what is the number before 4?
2
. How can we connect 2, n and the common difference +2 to write and algebraic expression?
2n + 2
. What is the 8 term of the sequence?
2(8) + 2 = 18
Position
Term
Rule
1
4
2
8
+4
3
12
+4
4
16
+4
5
20
+4
6
24
n
+4
. According to the pattern, what is the number before 4?
0
. How can we connect 4, n, and the common different 2 to write and algebraic expression?
4n
. What is the 32 term of the sequence?
4(32) = 128
Exercise :
Part A: Find an algebraic expression that can be used to find the nth term of each sequence.
1.
2.
3.
4.
3, 5, 7, 9……
5, 25, 125, 625…..
-1, -2, -3, …….
0, -2, -4,-6 …….
2n+1
5n
-n
-2n + 2
Part B : Measure Up Lesson 24 Sequence p.96
2
Proportional Linear Relationship to Non-Proportional Linear Relationship (notes)
Vocabulary : Linear – Ordered pair form a straight line on graph
Coordinate x – Independent variable
Coordinate y – Dependent variable
Ordered pair – (x , y)
Proportional Linear Relationship
Non- Proportional Linear Relationship
Straight line on graph going through the point
of origin (0,0)
Straight line on graph does not go through the
point of origin
Y = mx + 0
Y = mx – 0
Y = mx
Y = mx +b
Y = mx - b
Examples:
Position
Term
1
4
2
6
3
8
4
10
5
12
6
14
n
2n + 2
1. Identify the independent and dependent relationship between the term and its position
in the sequence
The result obtains on the term dependents on the assigned position
2. Using the information on number 1, change the independent variable to x and
dependent variable to y
Y = 2x +2 ,
where x = position n
y = term
3
3. Graph the relationship y = 2x +2
3. Give two evidence to identifying whether the sequence is proportional or nonproportional.
Non-proportional : Y = 2x + 2
Straight line does not go through the point of origin
4
Position
Term
1
4
2
8
3
12
4
16
5
20
6
24
n
4n
1. Identify the independent and dependent relationship between the term and its position in
the sequence
The result obtains on the term dependents on the assigned position
2. Using the information on number 1, change the independent variable to x and
dependent variable to y
Y = 4x ,
where x = position n
y = term
3. Graph the relationship y = 4x
3. Give two evidences identifying whether the sequence is proportional or nonproportional.
Proportional : Y = 4x
Straight line does go through the point of origin
Exercise : Fig 8 from TQ workshop #2
5