Warm-Up Write the next term in the series. Then write the series with summation notation. 5 n 3n -1 n=1.

Slides:

Advertisements

Similar presentations

Chapter 8 Vocabulary. Section 8.1 Vocabulary Sequences An infinite sequence is a function whose domain is the set of positive integers. The function.

Advertisements

Choi 2012 Arithmetic Sequence A sequence like 2, 5, 8, 11,…, where the difference between consecutive terms is a constant, is called an arithmetic sequence.

Arithmetic Sequences and Series days Digital Lesson.

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?

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.

I can identify and extend patterns in sequences and represent sequences using function notation. 4.7 Arithmetic Sequences.

EXAMPLE 1 Identify arithmetic sequences

 What are the next three terms in each sequence?  17, 20, 23, 26, _____, _____, _____  9, 4, -1, -6, _____, _____, _____  500, 600, 700, 800, _____,

1.1 Arithmetic Sequences and Series Warm-up (IN) 1.A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third.

Notes Over 11.3 Geometric Sequences

Arithmetic Sequences & Series Pre-Calculus Section.

9.2 Arithmetic Sequence and Partial Sum Common Difference Finite Sum.

12.2 – Analyze Arithmetic Sequences and Series. Arithmetic Sequence: The difference of consecutive terms is constant Common Difference: d, the difference.

Wednesday, March 7 How can we use arithmetic sequences and series?

Section 7.2 Arithmetic Sequences Arithmetic Sequence Finding the nth term of an Arithmetic Sequence.

12.2: Analyze Arithmetic Sequences and Series HW: p (4, 10, 12, 14, 24, 26, 30, 34)

Arithmetic Sequences and Series

THE BEST CLASS EVER…ERRR…. PRE-CALCULUS Chapter 13 Final Exam Review.

Homework Questions. Number Patterns Find the next two terms, state a rule to describe the pattern. 1. 1, 3, 5, 7, 9… 2. 16, 32, 64… 3. 50, 45, 40, 35…

Standard 22 Identify arithmetic sequences Tell whether the sequence is arithmetic. a. –4, 1, 6, 11, 16,... b. 3, 5, 9, 15, 23,... SOLUTION Find the differences.

Notes Over 11.2 Arithmetic Sequences An arithmetic sequence has a common difference between consecutive terms. The sum of the first n terms of an arithmetic.

Sequences & Series. Sequences  A sequence is a function whose domain is the set of all positive integers.  The first term of a sequences is denoted.

Geometric Sequences and Series Section Objectives Recognize, write, and find nth terms of geometric sequences Find the nth partial sums of geometric.

Notes Over 11.1 Sequences and Series A sequence is a set of consecutive integers. A finite sequence contains a last term Infinite sequences continue without.

4.7 Define & Use Sequences & Series. Vocabulary  A sequence is a function whose domain is a set of consecutive integers. If not specified, the domain.

Write the first six terms of the following sequences.

9.1 Sequences and Series. A sequence is a collection of numbers that are ordered. Ex. 1, 3, 5, 7, …. Finding the terms of a sequence. Find the first 4.

Lesson 8.1 Page #1-25(EOO), 33, 37, (ODD), 69-77(EOO), (ODD), 99, (ODD)

Change & Evaluate the following Logarithmic Equations to Exponential Equations.

Geometric Sequences & Series

Arithmetic Sequences & Series. Arithmetic Sequence: The difference between consecutive terms is constant (or the same). The constant difference is also.

8.3 Geometric Sequences and Series Objectives: -Students will recognize, write, and find the nth terms of geometric sequences. -Students will find the.

Essential Questions Series and Summation Notation

12.2, 12.3: Analyze Arithmetic and Geometric Sequences HW: p (4, 10, 12, 18, 24, 36, 50) p (12, 16, 24, 28, 36, 42, 60)

Thursday, March 8 How can we use geometric sequences and series?

11.3 Geometric Sequences & Series. What is a geometric sequence? What is the rule for a geometric sequence? How do you find the nth term given 2 terms?

1.2 Cont. Learning Objective: to continue to find terms of sequences and then to find the sum of a geometric series. Warm-up (IN) 1.Give the first 4 terms.

Algebra Arithmetic Sequences and Series. Vocabulary Sequence – A list of numbers in a particular order Arithmetic Sequence – A sequence of numbers.

Arithmetic Sequences and Series Section Objectives Use sequence notation to find terms of any sequence Use summation notation to write sums Use.

©2001 by R. Villar All Rights Reserved

Chapter 13: Sequences and Series

Homework Check.

The sum of the first n terms of an arithmetic series is:

Sequences and Series when Given Two Terms and Not Given a1

11.2 Arithmetic Sequences & Series

Geometric Sequences and Series (Section 8-3)

AKS 67 Analyze Arithmetic & Geometric Sequences

Arithmetic Sequences & Series

Bellwork Find the next two terms of each sequence.

Arithmetic Sequences and Series

Arithmetic Sequences and Series

5.3 Arithmetic Series (1/5) In an arithmetic series each term increases by a constant amount (d) This means the difference between consecutive terms is.

Chapter 12 – Sequences and Series

Arithmetic Sequences and Series

Sequences & Series.

Unit 1 Test #3 Study Guide.

12.2A Arithmetic Sequences

4-7 Sequences and Functions

10.2 Arithmetic Sequences and Series

Homework Check.

Homework Lesson 8.3 Page #1-17 (EOO), (ODD),

Homework Check.

Notes Over 11.1 Sequences and Series

Got ID? & AM7.1a To Identify an Arithmetic or Geometric Sequence and to Define Sequences and Series (Get the note taking guide from the.

Warm-Up Write the first five terms of an = 4n + 2 a1 = 4(1) + 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.

Questions over HW?.

Recognizing and extending arithmetic sequences

8-2 Analyzing Arithmetic Sequences and Series

Presentation transcript:

Warm-Up Write the next term in the series. Then write the series with summation notation. 5 n 3n -1 n=1

Agenda: 4/02/15 1.) Warm-up 2.) Questions: Objective: (1) Using and Writing Sequences (2) Using Series Agenda: 4/02/15 1.) Warm-up 2.) Questions: WS 11.1 Practice A #’s 1-27 ODD (Skip 11&13) WS 11.1 Practice B #’s 1-25 ODD (Skip 11) 3.) Lesson: 11.2 Arithmetic Sequences and Series 4.) Class/Homework 5.) Work in Pairs/Groups STAY ON TASK!!

11.2 Arithmetic Sequences and Series (Day 1) In an Arithmetic Sequence, the difference between consecutive terms is constant. The constant difference is called the common difference and is denoted by d. Ex. 1 Decide whether the sequence is arithmetic. Explain why or why not. - 3, 1, 5, 9, 13, … To decide whether a sequence is arithmetic, find the differences of consecutive terms. d = 1 – (- 3) = 4 d = 5 – 1 = 4 d = 9 – 5 = 4 d = 13 – 9 = 4 Each difference is 4, so the sequence is arithmetic.

11.2 Arithmetic Sequences and Series (Day 1) RULE FOR AN ARITHMETIC SEQUENCE The nth term of an arithmetic sequence with first term a1 and common difference d is given by: an = a1 + (n – 1)d Ex. 2 Write a rule for the nth term of the arithmetic sequence. Then find a25. 50, 44, 38, 32, … a1 = 50 and d = 44 – 50 = - 6, so the sequence is arithmetic. A rule for the nth term is: Memorize!!

11.2 Arithmetic Sequences and Series (Day 1) Ex. 3 Write a rule for the nth term of the arithmetic sequence. d = 4, a14 = 46 In order to write the nth term the “d” and the “a1” ARE NEEDED. To find a1 use the a14 and the following rule. an = a1 + (n – 1)d a14 = a1 + (14 – 1)(4) 46 = a1 + 52 - 6 = a1 an = - 6 + (n – 1)(4) an = - 6 + 4n – 4 an = 4n – 10 Memorize!!

11.2 Arithmetic Sequences and Series (Day 1) Ex. 4 Write a rule for the nth term of the arithmetic sequence. a5 = 17, a15 = 77 In order to find the nth term WE NEED to find the a1 and the d. We use the a5 and the a15 terms in the nth term for an arithmetic sequence. an = a1 + (n – 1)d Memorize!!

11.2 Arithmetic Sequences and Series (Day 1)

HOMEWORK This is FUN!!!!! Page 663 15 - 37 ALL