School starts at 7:15 for EOCT testing! May 10-13 and May 17-20: School starts at 7:15 for EOCT testing! Sequences 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. 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: Write the first six terms of the sequence defined by an = 4n + 5 Write the first six terms of the sequence defined by an = 2n2 – 1

Vocabulary Recursive Formula: an-1 Uses one or more previous terms to generate the next term. an-1

Example 2: A) Write the first six terms of the sequence where a1 = -2 and an = 2an-1 – 1 B) Write the first six terms of the sequence where a1 = 4 and an = 3an-1 + 5

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

Vocabulary Arithmetic Sequence: What is d? a2 – a1 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 Common difference an = a1 + (n – 1)d First term in the sequence What term you are looking for What term you are looking for

Example 1: d Find the 10th term of a1 = 7 and an = an-1 + 6

Example 2: Find the 10th term of the arithmetic sequence where a3 = -5 and a6 = 16 Find the 15th term of the arithmetic sequence where a5 = 7 and a10 = 22 Find the 12th term of the arithmetic sequence where a3 = 8 and a7 = 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: Find the 4 arithmetic means between 10 & -30

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

Vocabulary Geometric Sequence: What is r? 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

Formula for the nth term First term in the sequence an = a1rn-1 What term you are looking for What term you are looking for Common Ratio

Example 1 Find the 5th term of a1 = 8 and an = 3an-1

Example 2: Find a10 of the geometric sequence 12, 18, 27, 40.5, … Find a7 of the geometric sequence where a1 = 6 and r = 4

***Keep reviewing for your EOCT*** Homework P.140 #1-16 P.145 #1-17 ***Keep reviewing for your EOCT*** (May 10-11)

Warm up 1. Find the 8th term of the sequence defined by a1= –4 and an= an-1+ 2 2. Find the 12th term of the arithmetic sequence in which a4= 2 and a7= 6 3. Find the four arithmetic means between 6 and 26. 4. Find the 5th term on the sequence defined by a1= 2 and an= 2an-1.

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

Series Series: the sum of a sequence Summation Notation: EX. (for the above series)

= _______ + _______ + _______ + _______ = ____ + _____ + _____ + _____ = _____

Not in packet!! Summation Properties For sequences ak and bk and positive integer n: Not in packet!!

Summation Formulas For all positive integers n: Constant Linear Quadratic

Example 1: Evaluate

Extra Example: (Not in packet) Evaluate Homework: P.135 #18-24 *work on Benchmark Practice WS*

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

Formula for arithmetic series Vocabulary An Arithmetic Series is the sum of an arithmetic sequence. Formula for arithmetic series Sn=

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

Example 2: Given 3 + 12 + 21 + 30 + …, find S25

Example 3: Evaluate

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

Formula for geometric series Vocabulary An Geometric Series is the sum of an geometric sequence. Formula for geometric series Sn=

Example 1: Given the series 3 + 4.5 + 6.75 + 10.125 + …find S10 to the nearest tenth.

Example 2: n Evaluate r a1

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

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

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

Example 1: Find the sum of the infinite geometric series 3 + 1.2 + 0.48 + 0.192 + … 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:

Example 3: NOT IN PACKET Write 0.2 as a fraction in simplest form.

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