Download sequence

5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
1. 10 - e
2.
16
𝑓
3. 4e²
4. 8g - f
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
1. 10 - e
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
1. 10 - e
10 – 3
7
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
2.
16
𝑓
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
2.
16
𝑓
16
4
4
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
3. 4e²
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
3. 4e²
4(3)²
4·9
36
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
4. 8g - f
5 Minute Check
Find if d = 8, e = 3, f = 4 and g = -1. Complete
in your notes.
4. 8g - f
8 · (-1) – 4
-8–4
-12
Monday, May 11
Lesson 7.5.2
Sequences
Sequences
Objective: To describe the relationships and
extend terms in arithmetic sequences.
Sequences
A sequence is an ordered list of numbers.
Sequences
A sequence is an ordered list of numbers.
Each number in a sequence is a called a term.
Sequences
A sequence is an ordered list of numbers.
Each number in a sequence is a called a term.
In an arithmetic sequence, each term is found
by adding the same number to the previous
term.
Sequences
Describe the relationship between the terms in
the arithmetic sequence 8, 13, 18, 23, …. .
Then write the next three terms.
Sequences
Describe the relationship between the terms in
the arithmetic sequence 8, 13, 18, 23, …. .
Then write the next three terms.
8, 13, 18, 23,…….
+5 +5 +5
Each term is found by adding 5 to the
previous term.
The next three terms are 28, 33, 38
Sequences
Describe the relationship between the terms in
the arithmetic sequence 0.4, 0.6, 0.8, 1.0 , …. .
Then write the next three terms.
Sequences
Describe the relationship between the terms in
the arithmetic sequence 0.4, 0.6, 0.8, 1.0 , …. .
Then write the next three terms.
0.4, 0.6, 0.8, 1.0 , ….
+.2 +.2 +.2
Each term is found by adding 0.2 to the
previous term.
The next three terms are 1.2, 1.4 1.6
Sequences
Describe the relationship between the terms in
the arithmetic sequence 0, 13, 26, 39, …. .
Then write the next three terms.
Sequences
Describe the relationship between the terms in
the arithmetic sequence 0, 13, 26, 39, …. .
Then write the next three terms.
1, 13, 26, 39, ….
+13 +13 +13
Each term is found by adding 13 to the
previous term.
The next three terms are 52, 65, 78
Sequences
Describe the relationship between the terms in
the arithmetic sequence 1.0, 1.3, 1.6, 1.9, …. .
Then write the next three terms.
Sequences
Describe the relationship between the terms in
the arithmetic sequence 1.0, 1.3, 1.6, 1.9, …. .
Then write the next three terms.
1.0, 1.3, 1.6, 1.9, ….
+.3 +.3 +.3
Each term is found by adding 0.3 to the
previous term.
The next three terms are 2.2, 2.5, 2.8
Sequences
Describe the relationship between the terms in
the arithmetic sequence 52, 49, 46, 43, …. .
Then write the next three terms.
Sequences
Describe the relationship between the terms in
the arithmetic sequence 52, 49, 46, 43, …. .
Then write the next three terms.
52, 49, 46, 43, ….
-3
-3
-3
Each term is found by adding -3 to the
previous term.
The next three terms are 40, 37, 34
Sequences
Describe the relationship between the terms in
the arithmetic sequence 1,10,19,28, …. .
Then write the next three terms.
Sequences
Describe the relationship between the terms in
the arithmetic sequence 1,10,19,28, …. .
Then write the next three terms.
1,10,19,28, ….
+9 +9 +9
Each term is found by adding 9 to the
previous term.
The next three terms are 37, 46, 55
Sequences
Describe the relationship between the terms in
the arithmetic sequence -45, -39, -33, …. .
Then write the next three terms.
Sequences
Describe the relationship between the terms in
the arithmetic sequence -45, -39, -33, …. .
Then write the next three terms.
-45, -39, -33,, ….
+6
+6
Each term is found by adding 6 to the
previous term.
The next three terms are -27, -21, -15
Sequences
Describe the relationship between the terms in
𝟏 𝟏 𝟐 𝟓
, , , ,
𝟑 𝟐 𝟑 𝟔
the arithmetic sequence
write the next three terms.
…. . Then
Sequences
Describe the relationship between the terms in
𝟏 𝟏 𝟐 𝟓
the arithmetic sequence 𝟑, 𝟐, 𝟑, 𝟔, …. . Then
write the next three terms.
𝟏 𝟏 𝟐 𝟓
, , , , ….
𝟑 𝟐 𝟑 𝟔
𝟐 𝟑 𝟒 𝟓
, , ,
𝟔 𝟔 𝟔 𝟔
Each term is found by adding to the
previous term.
1
1
The next three terms are 1, 16, 13
1
6
Sequences
In a sequence, each term has a specific
position within the sequence. Consider the
sequence 2, 4, 6, 8, …..
Sequences
Notice that as the position number increases
by 1, the value of the term increases by 2.
Sequences
You can also write an algebraic expression to
represent the relationship between any term
in a sequence an its position in the sequence.
What is the expression for this sequence?
Sequences
You can also write an algebraic expression to
represent the relationship between any term
in a sequence an its position in the sequence.
What is the expression for this sequence? 2n
Sequences
The greeting cards that Meredith makes are sold in boxes
at a gift store. The first week, the store sold 5 boxes.
Each week the store sells five more boxes. The pattern
continues. What is the algebraic expression to represent
this situation? How many boxes will be sold at the end of
the 100th week?
Sequences
The greeting cards that Meredith makes are sold in boxes
at a gift store. The first week, the store sold 5 boxes.
Each week the store sells five more boxes. The pattern
continues. What is the algebraic expression to represent
this situation? How many boxes will be sold at the end of
the 100th week?
5n
After the 100th week;
5 · 100 = 500 boxes
Sequences
If the pattern continues, what algebraic
expression can be used to represent the
situation? How many circles will be in the 50th
figure?
Sequences
If the pattern continues, what algebraic
expression can be used to represent the
situation? How many circles will be in the 50th
figure?
3n
In the 50th figure;
3 · 50 = 150
Sequences
If the pattern continues, what algebraic
expression can be used to represent the
situation? How many circles will be in the 50th
figure?
Sequences
If the pattern continues, what algebraic
expression can be used to represent the
situation? How many circles will be in the 50th
figure?
2n + 1
In the 50th figure;
2 · 50 + 1 = 101
Sequences
What is the 10th term for the sequence below.
6, 12, 18, 24, ……
Sequences
What is the 10th term for the sequence below.
Term 1 2 3 4
6, 12, 18, 24, ……
6n; when n = 10
60
Sequences
What is the 20th term for the sequence below.
14, 28, 42, 56, ……
Sequences
What is the 20th term for the sequence below.
Term 1 2 3 4
14, 28, 42, 56, ……
14n; when n = 20
280
Sequences
Hannah has a doll collection. The table shows the
number of dolls she bought the first three years.
Suppose the pattern continues, what algebraic
expression can be used to represent the situation?
How many dolls will collect during the 25th year?
Sequences
Hannah has a doll collection. The table shows the
number of dolls she bought the first three years.
Suppose the pattern continues, what algebraic
expression can be used to represent the situation?
How many dolls will collect during the 25th year?
6n
In the 25h year;
6 · 25 = 150
Sequences
Write an algebraic expression to represent the
graph.
Sequences
Write an algebraic expression to represent the
graph.
3n
Sequences
Write an algebraic expression to represent the
graph.
Sequences
Write an algebraic expression to represent the
graph.
x+1
Or as an equation
y=x+1
Sequences
Write an algebraic expression to represent the
graph.
Sequences
Write an algebraic expression to represent the
graph.
x+5
Sequences
Write an algebraic expression to represent the
graph.
Sequences
Write an algebraic expression to represent the
graph.
x ÷ 2 or
𝑥
2
Sequences
Write an algebraic expression to represent the
graph.
Sequences
Write an algebraic expression to represent the
graph.
3x - 1
Sequences
Agenda Notes
No Homework –
Homework Practice 7.5.2
Due by the end of the period
Circle all answers and show all work
Chapter 7.5 Quiz
Friday, May 15