mondaytuesdaywednesdaythursdayfriday dec 3 unit 4 test dec 4 sequences & series dec 5 sequences...
TRANSCRIPT
MONDAY TUESDAYWEDNESDA
YTHURSDAY FRIDAY
DEC 3
UNIT 4 TEST
DEC 4
Sequences & Series
DEC 5
Sequences & Series
DEC 6
Post Test in Computer Lab
DEC 7
Sequences & Series
DEC 10
Unit 5 Review
DEC 11
UNIT 5 TEST
DEC 12
EXAM REVIEW
DEC 13
EXAM REVIEW
DEC 14
REVIEW
1st Period Final Exam
DEC 17EARLY RELEASE
4th / 2nd Exam
DEC 18EARLY RELEASE
5th / 3rd Exam
DEC 19EARLY RELEASE
6th / 7th Exam
Sequences and Series(Purple Book 4.7 – 4.9)
Tuesday Dec 4th,
Wednesday Dec 5th,
Friday Dec 6th
4.7 Sequences
Vocabulary• Sequence: an ordered list of numbers
– Ex: 3, 2, 1, 0, -1, -2
• Term: each number in a sequence– Ex: a1, a2, a3, a4, a5, a6
• Infinite Sequence: sequence that continues infinitely – Ex: 2, 4, 6, 8, …
• Finite Sequence: sequence that ends– Ex: 2, 4, 6
• Explicit Formula: defines the nth term of a sequence.
Example 1:
A) Write the first six terms of the sequence defined by an = 4n + 5
Example 1:
B. Write the first six terms of the sequence defined by an = 2n2 – 1
4.7 Series
Series• Series: the sum of a sequence
– Sequence: 1, 2, 3, 4– Series: 1 + 2 + 3 + 4
• Summation Notation:
4
1
12n
n
Summation Notation - __________________ EX. (for the above series)
4
1
12n
n
= _______ + _______ + _______ + _______
= ____ + _____ + _____ + _____ = _____
Example 3:
A) Evaluate
B) Evaluate
6
1
2k
k
6
1
4k
k
4.8 Arithmetic Sequences
MONDAY TUESDAYWEDNESDA
YTHURSDAY FRIDAY
DEC 3
UNIT 4 TEST
DEC 4
Sequences & Series
DEC 5
Sequences & Series
DEC 6
Post Test in Computer Lab
DEC 7
Sequences & Series
DEC 10
Unit 5 Review
DEC 11
UNIT 5 TEST
DEC 12
EXAM REVIEW
DEC 13
EXAM REVIEW
DEC 14
REVIEW
1st Period Final Exam
DEC 17EARLY RELEASE
4th / 2nd Exam
DEC 18EARLY RELEASE
5th / 3rd Exam
DEC 19EARLY RELEASE
6th / 7th Exam
Vocabulary
• Arithmetic Sequence: – A sequence generated by adding “d” a constant
number to pervious term to obtain the next term.– This number is called the common difference.
• What is d? a2 – a1
– 3, 7, 11, 15, … d = 4– 8, 2, -4, -10, … d = -6
Formula for the nth term
an = a1 + (n – 1)d
What term you are looking for
First term in the sequence
What term you are looking for
Common difference
Example 1:
A) Find the 10th term of a1 = 7 and an = an-1 + 6
B) Find the 7th term of a1 = 2.5 and an = an-1 - 3
d
Example 2:
A) Find the 10th term of the arithmetic sequence where a3 = -5 and a6 = 16
B. Find the 15th term of the arithmetic sequence where a5 = 7 and a10 = 22
• C. Find the 12th term of the arithmetic sequence where a3 = 8 and a7 = 20
Arithmetic & Geometric Sequences
Friday December 7th
MONDAY TUESDAYWEDNESDA
YTHURSDAY FRIDAY
DEC 7
Sequences & Series
DEC 10
Unit 5 Review
DEC 11
UNIT 5 TEST
DEC 12
EXAM REVIEW
DEC 13
EXAM REVIEW
DEC 14
REVIEW
1st Period Final Exam
DEC 17EARLY RELEASE
4th / 2nd Exam
DEC 18EARLY RELEASE
5th / 3rd Exam
DEC 19EARLY RELEASE
6th / 7th Exam
4.8 Arithmetic Series
Vocabulary
• An Arithmetic Series is the sum of an arithmetic sequence.
Formula for arithmetic series
Sn= 12 n
na a
Example 2:A) Given 3 + 12 + 21 + 30 + …, find S25
B) Given 16, 12, 8, 4, …, find S11
Example 3:
A) Evaluate12
1(6 2 )
kk
Example 3:
B) Evaluate21
1(5 4 )
kk
4.9 Geometric Sequences
Vocabulary
• Geometric Sequence:– A sequence generated by multiplying a constant
ratio to the previous term to obtain the next term.– This number is called the common ratio.
• What is r?
2, 4, 8, 16, … r = 2 27, 9, 3, 1, … r = 1/3
2
1
a
ra
Formula for the nth term
an = a1rn-1
What term you are looking for
First term in the sequence
What term you are looking for
Common Ratio
Example 1
A) Find the 5th term of a1 = 8 and an = 3an-1
B) Find the 7th term of a1 = 5 and an = 2an-1
Example 2:A) Find a10 of the geometric sequence 12,
18, 27, 40.5, …
B) Find a7 of the geometric sequence where a1 = 6 and r = 4
4.9 Geometric Series
Vocabulary
• An Geometric Series is the sum of an geometric sequence.
Formula for geometric series
Sn=
r1
r1a
n
1
Example 1:
• Given the series 3 + 4.5 + 6.75 + 10.125 + …find S10 to the nearest tenth.
Example 2:
• Evaluate1
7
14( 5)k
k
n
a1r
Example 2:
• Evaluate 16
132 k
k
n
a1r