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

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

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

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

Geometric Sequences and Series

Arithmetic Sequences and Series

Arithmetic Sequences and Partial Sums

Arithmetic Sequences & Partial Sums Pre-Calculus Lesson 9.2.

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.

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.

Sequences and Series 13.3 The arithmetic sequence

Sequences and Series (T) Students will know the form of an Arithmetic sequence.  Arithmetic Sequence: There exists a common difference (d) between each.

Section 11-1 Sequences and Series. Definitions A sequence is a set of numbers in a specific order 2, 7, 12, …

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

Pre-Calculus Section 8.2B Arithmetic Sequences

Ch.9 Sequences and Series

Arithmetic Sequences and Series

Geometric Sequences and Series

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

Sequences Definition - A function whose domain is the set of all positive integers. Finite Sequence - finite number of values or elements Infinite Sequence.

Introduction to sequences and series

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.

9-4 Arithmetic Series Today’s Objective: I can find the sum of an arithmetic series.

9.2 Arithmetic Sequences. Objective To find specified terms and the common difference in an arithmetic sequence. To find the partial sum of a arithmetic.

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.

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.

By the end of the section students will be able to find determine whether a sequence is arithmetic, find the n th term of an arithmetic sequence, find.

Do Now What do you notice about the sums of these sequences?

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

Section 12-1 Sequence and Series

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 1 Definition of Sequence You find a job that pays an annual salary of $32,000 with an.

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

11/5/ Arithmetic Series. 11/5/ Series Series – The sum of terms of a sequence Infinite Series – The sum of all terms in a sequence Finite.

Warm up 1. Find the sum of : 2. Find the tenth term of the sequence if an = n2 +1: =

Geometric Sequences & Series

Ch.9 Sequences and Series

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

Series Section Intro to Series Series A sum of the terms of a sequence is called a series. A series is a finite series if it is the sum of a finite.

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

Sum of Arithmetic Sequences. Definitions Sequence 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.

A LESSON BY U S PRAJAPATI, PGT MATH, KV KHAGAUL GEOMETRIC SEQUENCES AND SERIES.

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.

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

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

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

Section 8.2 Arithmetic Sequences & Partial Sums. Arithmetic Sequences & Partial Sums A sequence in which a set number is added to each previous term is.

Arithmetic Sequences & Partial Sums

Arithmetic Sequences and Series

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 Sequences & Series

Arithmetic Sequences and Series

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 ?

Arithmetic and Geometric

Unit 1 Test #3 Study Guide.

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

Sequences and Series.

Geometric Sequences and Series

Geometric Sequence Skill 38.

Geometric Sequences and Series

Geometric Sequences and Series

Chapter 9 Section 1 (Series and Sequences)

Presentation transcript:

Ch.9 Sequences and Series Section 4 –Arithmetic Series

Definitions: Series: the sum of the terms of a sequence. Finite Series: has a first and last term. Infinite Series: Continues without end.

EXample Finite Sequence Finite Series 6,9,12,15, =(60) Infinite Sequence Infinite Series 3,7,11,15,… …

Definition: Arithmetic Series

EXample What is the sum of the even integers from 2 to 100?

EXample A company pays a bonus to salespeople at the end of their first 50 weeks if they make 10 sales in their first week and, then improve their sales by two each week thereafter. How many sales would someone need to get the bonus?