Unit 6: Sequences & Series

Slides:



Advertisements
Similar presentations
OBJECTIVE We will find the missing terms in an arithmetic and a geometric sequence by looking for a pattern and using the formula.
Advertisements

The sum of the infinite and finite geometric sequence
Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?
CN College Algebra Ch. 11: Sequences 11.3: Geometric Sequences Goals: Determine if a sequence is geometric. Find a formula for a geometric sequence. Find.
Warm-up Finding Terms of a Sequence
Last Time Arithmetic SequenceArithmetic Series List of numbers with a common difference between consecutive terms Ex. 1, 3, 5, 7, 9 Sum of an arithmetic.
Determine whether the sequence 6, 18, 54, is geometric. If it is geometric, find the common ratio. Choose the answer from the following :
Arithmetic Sequences Section 4.5. Preparation for Algebra ll 22.0 Students find the general term and the sums of arithmetic series and of both finite.
Sec 11.3 Geometric Sequences and Series Objectives: To define geometric sequences and series. To define infinite series. To understand the formulas for.
13.7 Sums of Infinite Series. The sum of an infinite series of numbers (or infinite sum) is defined to be the limit of its associated sequence of partial.
12.2 – Analyze Arithmetic Sequences and Series. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference.
State whether the sequence below is arithmetic, geometric or neither and then write the explicit definition of the sequence. 3, 7, 11, 15...
12.2: Analyze Arithmetic Sequences and Series HW: p (4, 10, 12, 14, 24, 26, 30, 34)
11.4 Series & Sigma Notation
Pg. 417/425 Homework Pg. 395#43, 60 Pg. 589#1 – 8 all, 17, 18, 21, 22.
Notes Over 11.4 Infinite Geometric Sequences
SEQUENCES AND SERIES Arithmetic. Definition A series is an indicated sum of the terms of a sequence.  Finite Sequence: 2, 6, 10, 14  Finite Series:2.
SERIES AND CONVERGENCE
Ch. 11 – Sequences & Series 11.1 – Sequences as Functions.
Today in Precalculus Notes: Sequences Homework Go over quiz.
Review for the Test Find both an explicit formula and a recursive formula for the nth term of the arithmetic sequence 3, 9, 15,……… Explicit Formula ______________________________.
Series Ch. 13.
13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…
11-4 INTRO TO SERIES DEFINITION A SERIES IS THE SUM OF THE TERMS OF A SEQUENCE. SEQUENCE VS. SERIES 2, 4, 8, … …
Homework Questions. Geometric Sequences In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.
13.4 Geometric Sequences and Series Example:3, 6, 12, 24, … This sequence is geometric. r is the common ratio r = 2.
Pg. 417/425 Homework Pg. 395#43, 60 Find the “derivative” of y = sin x Pg. 589#1 – 8 all, 17, 18, 21, 22 #23 #85Graph #860 < Ɵ < π #87Ɵ = = 54.72°
8.3 Geometric Sequences and Series Objectives: -Students will recognize, write, and find the nth terms of geometric sequences. -Students will find the.
SERIES: PART 1 Infinite Geometric Series. Progressions Arithmetic Geometric Trigonometric Harmonic Exponential.
Figure out how to work with infinite series when i=0 vs i=1 Slide 12.
Geometric Series. In a geometric sequence, the ratio between consecutive terms is constant. The ratio is called the common ratio. Ex. 5, 15, 45, 135,...
{ 12.3 Geometric Sequence and Series SWBAT evaluate a finite geometric series SWBAT evaluate infinite geometric series, if it exists.
Lesson 7-7 Geometric Sequences.  Remember, an arithmetic sequence changes by adding (or subtracting) a constant to each term.  Ex: -4, 1, 6, 11, 16,
Arithmetic and Geometric Sequences. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 1. 7, 13, 19, 25, …2.
How do I find the sum & terms of geometric sequences and series?
Thursday, March 8 How can we use geometric sequences and series?
9.3 Geometric Sequences and Series. 9.3 Geometric Sequences A sequence is geometric if the ratios of consecutive terms are the same. This common ratio.
12.3 – Analyze Geometric Sequences and Series. Geometric Sequence: Ratio of any term to the previous term is constant Common Ratio: Ratio each term is.
13.3 Arithmetic and Geometric Series and Their Sums Finite Series.
9.3 Geometric Sequences and Series. Common Ratio In the sequence 2, 10, 50, 250, 1250, ….. Find the common ratio.
Se quences Recursive Definition Ch. 13 (2). Warm Up Find the first 4 terms of the sequence. State whether it is arithmetic, geometric or neither
Pre-Calculus Section 8.1A Sequences and Series. Chapter 8: Sequences, Series, and Probability Sequences and series describe algebraic patterns. We will.
Unit 4: Sequences & Series 1Integrated Math 3Shire-Swift.
Chapter 13: Sequences and Series
Series and Convergence (9.2)
Geometric Sequences and Series
11.3 – Geometric Sequences and Series
13.3 – Arithmetic and Geometric Series and Their Sums
Warm-up Problems Consider the arithmetic sequence whose first two terms are 3 and 7. Find an expression for an. Find the value of a57. Find the sum of.
Aim: What is the geometric series ?
Unit 1 Test #3 Study Guide.
Sequences and Series Day 7
Homework Lesson 8.3 Page #1-17 (EOO), (ODD),
ex. 2, 7, 12, 17, 22, 27 5 is the common difference. an+1 = an + d
Sequences and Series.
Arithmetic Sequences:
Geometric Sequences and Series
Warm Up Look for a pattern and predict the next number or expression in the list , 500, 250, 125, _____ 2. 1, 2, 4, 7, 11, 16, _____ 3. 1, −3,
Warm up 1. One term of a geometric sequence is a5 = 48. The common ratio is r = 2. Write a rule for the nth term. 2. Find the sum of the geometric.
Got ID? & AM7.1a To Identify an Arithmetic or Geometric Sequence and to Define Sequences and Series (Get the note taking guide from the.
9.5 Series.
Warmup Solve cos 2
Got ID? & AM7.1a To Identify an Arithmetic or Geometric Sequence and to Define Sequences and Series (Get the note taking guide from the.
Section 2 – Geometric Sequences and Series
Geometric Sequence Skill 38.
Geometric Sequences and Series
Warm Up Use summation notation to write the series for the specified number of terms …; n = 7.
Warm Up Write the first 4 terms of each sequence:
Geometric Sequences and Series
How many tiles did he add? INTRO TO SEQUENCES AND SERIES Guido wants to create a tile mosaic around the Ram-Fountain. In the first week he begins.
Presentation transcript:

Unit 6: Sequences & Series Sec 1: Arithmetic & Geometric Sequences Homework: pg 663 #1-20 Learning Target: I will find the pattern in a sequence and determine if it is arithmetic, geometric or neither

Ex 1: Using a Pattern in Real Life Answer: C

Define the Following (pg 659): Major Terms for the Unit Definition Example Sequence Arithmetic Sequence Common Difference Geometric Sequence Common Ratio Minor Terms for the Unit Definition Example Term Finite Sequence Infinite Sequence

Ex 2: Identifying Arithmetic Sequences Determine whether each sequence is Arithmetic: 5, -6, -17, -28,… -4, 12, 28, 42, … -6, 3, 12, 21,…

Ex 3: Identifying Geometric Sequence Determine whether each sequence is geometric. -2, 6, -18, 54, … 8, 16, 24, 32, … -8, 2, -0.5, 0.125, …

Ex 4: Finding a Pattern Find the pattern and give the next 4 terms. Tell if the sequence is arithmetic, geometric or neither. 16, 24, 36, 54, … 1, 4, 9, 16, … 23, 17, 11, 5, …

Stump Your Buddy: Create your own sequence. When you are finished, exchange your sequence with a friend a find each other’s pattern. You will: Find the next 4 terms. Determine if the sequence is arithmetic, geometric or neither.

HOMEWORK Pg 663 #1-20