Name: ___________________
ID: ______________________
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?
. How can we connect 2, n and the common difference +2 to write and algebraic expression?
. What is the 8 term of the sequence?
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?
. How can we connect 4, n, and the common different 2 to write and algebraic expression?
. What is the 32 term of the sequence?
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 …….
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
2. Using the information on number 1, change the independent variable to x and
dependent variable to y
3
3. Graph the relationship y = 2x +2
3. Give two evidence to show that the sequence is proportional or non-proportional.
Position
1
2
3
4
5
6
n
4
Term
4
8
12
16
20
24
4n
1. Identify the independent and dependent relationship between the term and its position in
the sequence
2. Using the information on number 1, change the independent variable to x and
dependent variable to y
3. Graph the relationship y = 4x
3. Give two evidences identifying whether the sequence is proportional or nonproportional.
Exercise : Fig 8 from TQ workshop #2
5