May 10-13 and May 17-20:
School starts at 7:15 for
EOCT testing!
EOCT: May 10-11

Vocabulary
• Sequence: an ordered list of numbers
– Ex. -2, -1, 0, 1, 2, 3
• Term: each number in a sequence
– Ex. a
1
, a
2
, a
3
, a
4
, a
5
, a
6
• 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 a n
= 4n + 5
B) Write the first six terms of the sequence defined by a n
= 2n 2 – 1

Vocabulary
• Recursive Formula:
– Uses one or more previous terms to generate the next term. a n-1

Example 2:
A) Write the first six terms of the sequence where a
1
= -2 and a n
= 2a n-1
– 1
B) Write the first six terms of the sequence where a
1
= 4 and a n
= 3a n-1
+ 5

May 10-13 and May 17-20:
School starts at 7:15 for
EOCT testing!
EOCT: May 10-11

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? a
2
– 3, 7, 11, 15, …
– a
1
– 8, 2, -4, -10, … d = 4 d = -6

Formula for the n th term
Common difference
First term in the sequence a n
= a
1
+ (n – 1)d
What term you are looking for
What term you are looking for

Example 1:
A) Find the 10 th term of a
1 a n
= a n-1
+ 6
= 7 and d
B) Find the 7 th term of a
1 a n
= a n-1
- 3
= 2.5 and

Example 2:
A) Find the 10 th term of the arithmetic sequence where a
3
= -5 and a
6
= 16
B) Find the 15 th term of the arithmetic sequence where a
5
= 7 and a
10
= 22
C) Find the 12 th term of the arithmetic sequence where a
3
= 8 and a
7
= 20

Vocabulary
• Arithmetic Means:
– Terms in between 2 nonconsecutive terms
– Ex. 5, 11, 17, 23, 29  11, 17, 23 are the arithmetic means between 5 & 29

Example 3:
A) Find the 4 arithmetic means between
10 & -30
B) Find the 5 arithmetic means between
6 & 60

May 10-13 and May 17-20:
School starts at 7:15 for
EOCT testing!
EOCT: May 10-11

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?
a
2 a
1
 r
– 2, 4, 8, 16, …
– 27, 9, 3, 1, … r = 2 r = 1/3

Formula for the n th term
First term in the sequence a n
= a
1 r n-1
What term you are looking for
Common Ratio
What term you are looking for

Example 1
• Find the 5 th term of a
1
= 8 and a n
= 3a n-1
• Find the 7 th term of a
1
= 5 and a n
= 2a n-1

Example 2:
A) Find a
10 of the geometric sequence
12, 18, 27, 40.5, …
B) Find a
7 a
1 of the geometric sequence where
= 6 and r = 4

P.140 #1-16
P.145 #1-17

1. Find the 8 th term of the sequence defined by a
1
= –4 and a n
= a n-1
+ 2
2. Find the 12 th term of the arithmetic sequence in which a
4
= 2 and a
7
= 6
3. Find the four arithmetic means between 6 and 26.
4. Find the 5 th term on the sequence defined by a
1
= 2 and a n
= 2a n-1
.

May 10-13 and May 17-20:
School starts at 7:15 for
EOCT testing!
( M2 )
EOCT: May 10-11

• 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: n
4


1
2 n

1

n
4


1
2 n

1
= _______ + _______ + _______ + _______
= ____ + _____ + _____ + _____ = _____

Summation Properties
• For sequences a k and b k and positive integer n :
1) k n 

1 ca k
 c a k k n 

1
2) k n 

1
 a k
 b k
  k n  

1 a k
 n

1 k b k

Summation Formulas
• For all positive integers n :
Constant k n 

1 c
 nc k n 

1 k n 

1 k
2 
Quadratic
(

1)(2 n

1)
6 k
Linear

(

1)
2

Example 1:
A) Evaluate k
6


1
2 k
B) Evaluate 4 k
6


1 k

Extra Example:
• Evaluate m
5 

1
(
)
(2 m
2 
3 m

2)
Homework:
P.135 #18-24
*work on Benchmark Practice WS*

May 10-13 and May 17-20:
School starts at 7:15 for
EOCT testing!
( M2 )
EOCT: May 10-11
Sequences and Series Test: May 18

Vocabulary
• An Arithmetic Series is the sum of an arithmetic sequence.
Formula for arithmetic series
S n
= n

 a a n
2 



Example 1:
A.
Find the series 1, 3, 5, 7, 9, 11
B. Find the series 8, 13, 18, 23, 28, 33, 38

Example 2:
A) Given 3 + 12 + 21 + 30 + …, find S
25
B) Given 16, 12, 8, 4, …, find S
11

A) Evaluate k
12 

1
Example 3:
B) Evaluate k
21 

1

May 10-13 and May 17-20:
School starts at 7:15 for
EOCT testing!
( M2 )
EOCT: May 10-11
Sequences and Series Test: May 18

Vocabulary
• An Geometric Series is the sum of an geometric sequence.
S n
= a
1



1

1
 r n r 



Example 1:
• Given the series
3 + 4.5 + 6.75 + 10.125 + …find S
10 to the nearest tenth.

n
• Evaluate
Example 2: k
7 

1
4( 5) k

1 r a
1
• Evaluate k
6 

1
2

• P. 141 #16-27
• P. 145 #18-23
• Study/Review for EOCT!
( Sequences and Series ARE ON the EOCT )

May 10-13 and May 17-20:
School starts at 7:15 for
EOCT testing!
( M2 )
Sequences and Series Test: May 18
Finals:
1 st Period – May 21
2 nd Period – May 24
6 th Period – May 26

Vocabulary
• An Infinite Geometric Series is a geometric series with infinite terms.
S =
( 1 a
1
 r )
If
 r

<1 then the _______ can be found
If
 r

>1 then the _______ cannot be found

Example 1:
A) Find the sum of the infinite geometric series 3 + 1.2 + 0.48 + 0.192 + …
B) Find the sum of the infinite geometric series 8 + 9.6 + 11.52 + 13.824 + …

Example 2:
• Find the sum of the infinite geometric series below: k



1
1
3 k

1

Example 3:
A. Write 0.2 as a fraction in simplest form.
B. Write 0.04 as a fraction in simplest form.

Homework
• P. 147 #32 – 45 (M2 – Purple )