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