Geometric Sequences and Series

Slides:

Advertisements

Similar presentations

Algebra II Honors—Day 69. Warmup Solve and check: Find the next four terms of this arithmetic sequence: 207, 194, 181,... Find the indicated term of this.

Advertisements

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

What is the sum of the following infinite series 1+x+x2+x3+…xn… where 0

Geometric Sequences and Series

11.4 – Infinite Geometric Series. Sum of an Infinite Geometric Series.

The sum of the infinite and finite geometric sequence

Assignment Answers: Find the partial sum of the following: 1. = 250/2 ( ) = 218, = 101/2 (1/2 – 73/4) = Find the indicated n th.

9-3 Geometric Sequences & 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.

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.

11.4 Geometric Sequences Geometric Sequences and Series geometric sequence If we start with a number, a 1, and repeatedly multiply it by some constant,

Arithmetic Sequences and Series Sequences Series List with commas “Indicated sum” 3, 8, 13,

Aim: What are the arithmetic series and geometric series? Do Now: Find the sum of each of the following sequences: a)

Geometric Sequences and Series

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

Notes Over 11.4 Infinite Geometric Sequences

10.2 – Arithmetic Sequences and Series. An introduction … describe the pattern Arithmetic Sequences ADD To get next term Geometric Sequences MULTIPLY.

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.

ADVANCED ALG/TRIG Chapter 11 – Sequences and Series.

12.4 – Find Sums of Infinite Geometric Series. Think about this… What will happen when n becomes really big? It will get closer and closer to zero.

13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…

Ch.9 Sequences and Series Section 4 –Arithmetic Series.

Section 12-1 Sequence and Series

12.3 Geometric Sequences and Series ©2001 by R. Villar All Rights Reserved.

Geometric Sequences & Series

SERIES: PART 1 Infinite Geometric Series. Progressions Arithmetic Geometric Trigonometric Harmonic Exponential.

Copyright © 2011 Pearson, Inc. 9.5 Series Goals: Use sigma notation to find the finite sums of terms in arithmetic and geometric sequences. Find sums of.

{ 12.3 Geometric Sequence and Series SWBAT evaluate a finite geometric series SWBAT evaluate infinite geometric series, if it exists.

SECTION REVIEW Arithmetic and 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.

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.

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

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

Section 12.3 – Infinite Series. 1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2,

13.5 – Sums of Infinite Series Objectives: You should be able to…

Arithmetic Sequences.

12.1 – Arithmetic Sequences and Series

Arithmetic and Geometric

Arithmetic and Geometric Means

The sum of the infinite and finite geometric sequence

11.3 – Geometric Sequences and Series

13.3 – Arithmetic and Geometric Series and Their Sums

Arithmetic and Geometric Series

Arithmetic Sequences and Series

Aim: What is the geometric series ?

Infinite Geometric Series

Arithmetic and Geometric

Chapter 12 – Sequences and Series

Unit 1 Test #3 Study Guide.

12.3 – Geometric Sequences and Series

10.2 Arithmetic Sequences and Series

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

Unit 5 – Series, Sequences, and Limits Section 5

12.2 – Arithmetic Sequences and Series

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

12.2 – Arithmetic Sequences and Series

12.3 – Geometric Sequences and Series

Geometric Sequences and series

Section 2 – Geometric Sequences and Series

Geometric Sequence Skill 38.

Unit 5 – Series, Sequences, and Limits Section 5

Warm Up Use summation notation to write the series for the specified number of terms …; n = 7.

12.2 – Geometric Sequences and Series

12.1 – Arithmetic Sequences and Series

62 – Arithmetic and Geometric Sequences Calculator Required

Unit 13 Pretest.

Presentation transcript:

Geometric Sequences and Series

Vocabulary of Sequences (Universal)

Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 – 2 vs. 9/2 – 3… not arithmetic

1/2 x 9 NA 2/3

Find two geometric means between –2 and 54 -2, ____, ____, 54 -2 54 4 NA x The two geometric means are 6 and -18, since –2, 6, -18, 54 forms an geometric sequence

-3, ____, ____, ____

x 9 NA

Since this represents the first term, We must multiply by r to get 2nd term

1/2 7 x

Section 12.3 – Infinite Series

1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2, 4, 8, … Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible:

Find the sum, if possible: