MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
DEC 3
DEC 4
DEC 5
DEC 6
UNIT 4 TEST
Sequences &
Series
Sequences &
Series
Post Test in
Sequences &
Computer Lab Series
DEC 10
DEC 11
DEC 12
DEC 13
Unit 5 Review
UNIT 5 TEST
EXAM
REVIEW
EXAM
REVIEW
DEC 17
EARLY
RELEASE
DEC 18
EARLY
RELEASE
DEC 19
EARLY
RELEASE
4th / 2nd Exam
5th / 3rd Exam
6th / 7th Exam
DEC 7
DEC 14
REVIEW
1st Period
Final 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 - __________________
EX. (for the above series)
• Summation Notation:
4
 2n  1
n 1
4
 2n  1
n1
= _______ + _______ + _______ + _______
= ____ + _____ + _____ + _____ = _____
Example 3:
A) Evaluate
6
 2k
k 1
6
B) Evaluate 4  k
k 1
4.8 Arithmetic Sequences
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
DEC 3
DEC 4
DEC 5
DEC 6
UNIT 4 TEST
Sequences &
Series
Sequences &
Series
Post Test in
Sequences &
Computer Lab Series
DEC 10
DEC 11
DEC 12
DEC 13
Unit 5 Review
UNIT 5 TEST
EXAM
REVIEW
EXAM
REVIEW
DEC 17
EARLY
RELEASE
DEC 18
EARLY
RELEASE
DEC 19
EARLY
RELEASE
4th / 2nd Exam
5th / 3rd Exam
6th / 7th Exam
DEC 7
DEC 14
REVIEW
1st Period
Final 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, …
8, 2, -4, -10, …
d=4
d = -6
Formula for the nth term
First term in the
sequence
Common difference
an = a1 + (n – 1)d
What term you are
looking for
What term you are
looking for
Example 1:
A) Find the 10th term of a1 = 7 and
an = an-1 + 6
d
B) Find the 7th term of a1 = 2.5 and
an = an-1 - 3
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
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
DEC 7
Sequences &
Series
DEC 10
DEC 11
DEC 12
DEC 13
Unit 5 Review
UNIT 5 TEST
EXAM
REVIEW
EXAM
REVIEW
DEC 17
EARLY
RELEASE
DEC 18
EARLY
RELEASE
DEC 19
EARLY
RELEASE
4th / 2nd Exam
5th / 3rd Exam
6th / 7th Exam
DEC 14
REVIEW
1st Period
Final Exam
4.8 Arithmetic Series
Vocabulary
• An Arithmetic Series is the sum of an arithmetic
sequence.
Formula for arithmetic series
Sn=
n
 a1  an 
2
Example 2:
A) Given 3 + 12 + 21 + 30 + …, find S25
B) Given 16, 12, 8, 4, …, find S11
Example 3:
12
A) Evaluate
(6  2k )

k 1
Example 3:
21
B) Evaluate
(5  4k )

k 1
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.
a2
r
• What is r?
a1
 2, 4, 8, 16, …
 27, 9, 3, 1, …
r=2
r = 1/3
Formula for the nth term
First term in the
sequence
an =
What term you are
looking for
n-1
a1r
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= a  1  r


1
 1 r 
n
Example 1:
• Given the series
3 + 4.5 + 6.75 + 10.125 + …find S10 to the
nearest tenth.
Example 2:
n
7
k 1
4(

5)
• Evaluate 
k 1
a1
r
Example 2:
n
6
• Evaluate
k 1
2
3
  
k 1
a1
r