Download 8.1.notebook April 07, 2016

8.1.notebook
April 07, 2016
Lesson 8.1 Essential Question: How can sequences and series and their characteristics be used to solve problems?
Objective: Define and use sequences and series.
Standards: IF.A.3
Agenda:
• Warm‐up
• Go over HW
• Go over task
• IWhere we're headed...
• Sequences
• Series
Summary: What does the uppercase Greek letter sigma, written Ʃ, stand for?
Homework: Exploration 1 #1 (Journal p. 216‐217)
8.1.notebook
April 07, 2016
Warm-up 4/7/16
List the next three terms of the function, then try to write an
equation for the function.
x
y
5
1
2
2
7
2
4
3
9
3
8
1. x
y
1
2.
4
4
5
5
6
6
8.1.notebook
April 07, 2016
Homework Questions? p. 470 #1-10
8.1.notebook
April 07, 2016
Unit 3 Task:
19 points possible
+
6 points for rubric
=
25 points
8.1.notebook
April 07, 2016
Where we're headed...
Today: begin Unit 4a, Sequences and Series
Chapter 8 in textbook
Progress Report Coming Soon - Last day for makeup work 4/14
Unit 4a Test 4/27-4/28
8.1.notebook
April 07, 2016
8.1 Defining and Using Sequences and Series
Sequence: an ordered list of numbers
Domain: typically positive integers 1,2,3,4,...,n
Range: the terms of the sequence
Domain
1 2 3 4 ... n
Range
a1 a2 a3 a4 ... an
8.1.notebook
April 07, 2016
8.1 Defining and Using Sequences and Series
Example 1: Writing Terms
Together: Write the first six terms of an = (-3)
n-1
On your own: Write the first six terms of f(n) = 2n + 5
8.1.notebook
April 07, 2016
8.1 Defining and Using Sequences and Series
Example 2: Writing Rules
Together: Describe the pattern, write the next term, and write a
rule for the nth term of the sequence: -1, -8, -27, -64, ...
Together: Describe the pattern, write the next term, and write a
rule for the nth term of the sequence: 0, 2, 6, 12, ...
8.1.notebook
April 07, 2016
8.1 Defining and Using Sequences and Series
Example 2: Writing Rules cont.
On your own: Describe the pattern, write the next term, and
write a rule for the nth term of the sequence:
a) 3,5,7,9,...
b) 3,8,15,24,...
8.1.notebook
Journal Page 220 #1-4
April 07, 2016
Foreseer
2
Concluder 3
Facilitator 4
Naysayer 5
Presenter 1
Lucky #
8.1.notebook
April 07, 2016
8.1 Defining and Using Sequences and Series
Series: when the terms of a sequence are added together
Finite Series: a series with a specific number of terms
ex. 2+4+6+8
Infinite Series: a series without a specific number of terms
ex. 2+4+6+8+...
Summation Notation (Sigma Notation): used to write a series
4
ex. 2+4+6+8 =
2i
Ʃ
i=1
∞
ex. 2+4+6+8+... = Ʃ 2i
i=1
8.1.notebook
April 07, 2016
8.1 Defining and Using Sequences and Series
upper limit of summation
upper limit of summation
∞
4
2+4+6+8 =
2i
Ʃ
i=1
index of summation
2+4+6+8+... =
pattern/function
Ʃ 2i
pattern/function
i=1
index of summation
lower limit of summation
lower limit of summation
Example 3: Writing Series using summation notation
Together: Write each series using summation notation.
a) 25 + 50 + 75 + ... + 250
b)
1
2
3
4
/2 + /3 + /4 + /5 +...
On your own: Write each series using summation notation.
a)
5 + 10 + 15 + ... + 100
b)
6 + 36 + 216 + 1296 +...
8.1.notebook
April 07, 2016
8.1 Defining and Using Sequences and Series
upper limit of summation
upper limit of summation
∞
4
2+4+6+8 =
2i
Ʃ
i=1
index of summation
2+4+6+8+... =
pattern
Ʃ 2i
pattern
i=1
lower limit of summation
index of summation
Example 4: Finding the sum of a series
8
Together: Find the sum
Ʃ(3+k ) .
2
k=4
9
On your own: Find the sum
(4k­1) .
Ʃ
k=3
lower limit of summation
8.1.notebook
Journal Page 220 #5-7
April 07, 2016
Foreseer
3
Concluder 4
Facilitator 5
Naysayer 1
Presenter 2
Lucky #
8.1.notebook
April 07, 2016
Summary: What does the uppercase Greek letter sigma, written Ʃ, stand for?
Homework: Exploration 1 #1 (Journal p. 216‐217)