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

Slides:

Advertisements

Similar presentations

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?

Advertisements

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.

Geometric Sequences and Series

Notes Over 11.3 Geometric Sequences

Unit 7: Sequences and Series. Sequences A sequence is a list of #s in a particular order If the sequence of numbers does not end, then it is called an.

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.

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,

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

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

Arithmetic Sequences and Series

Geometric Sequences and Series

Notes Over 11.4 Infinite Geometric Sequences

Find each sum:. 4, 12, 36, 108,... A sequence is geometric if each term is obtained by multiplying the previous term by the same number called the common.

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.

13.3 Arithmetic and Geometric Series and Their Sums

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.

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

Section 12-1 Sequence and Series

Review of Sequences and Series.  Find the explicit and recursive formulas for the sequence:  -4, 1, 6, 11, 16, ….

13.4 Geometric Sequences and Series Example:3, 6, 12, 24, … This sequence is geometric. r is the common ratio r = 2.

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

Geometric Sequences & Series

Section Finding sums of geometric series -Using Sigma notation Taylor Morgan.

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,...

Arithmetic and Geometric Sequences. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 1. 7, 13, 19, 25, …2.

11.2 Arithmetic Series. What is a series?  When the terms of a sequence are added, the indicated sum of the terms is called a series.  Example  Sequence.

Review of 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.

Warm -up Suppose angle A is acute and. Find sin2A and cos 2A.

Honors Precalculus Day 3 Section 11.3 Geometric Sequences The end of new material…BOO!!! 3/12/2016.

Geometric Sequence – a sequence of terms in which a common ratio (r) between any two successive terms is the same. (aka: Geometric Progression) Section.

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.

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.

Sequences and Series Adaped from teacherweb.com. Introduction to Sequences and Series  Sequence – 1) an ordered list of numbers. 2) a function whose.

Review on Sequences and Series-Recursion/Sigma Algebra II.

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

Holt McDougal Algebra 2 Geometric Sequences and Series Holt Algebra 2Holt McDougal Algebra 2 How do we find the terms of an geometric sequence, including.

Chapter 8: Sequences and Series Lesson 4: Geometric Series Mrs. Parziale.

Homework Check.

Geometric Sequences and Series

Arithmetic and Geometric

11.3 – Geometric Sequences and Series

13.3 – Arithmetic and Geometric Series and Their Sums

Geometric Sequences and Series (Section 8-3)

Ch. 8 – Sequences, Series, and Probability

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.

Geometric Series When the terms of a geometric sequence are added, the result is a geometric series The sequence 3, 6, 12, 24, 48…gives rise to the series.

Aim: What is the geometric series ?

Arithmetic and Geometric

Chapter 12 – Sequences and Series

Unit 1 Test #3 Study Guide.

Finite Geometric Series

10.2 Arithmetic Sequences and Series

Homework Check.

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

Unit 5 – Series, Sequences, and Limits Section 5

ex. 2, 7, 12, 17, 22, 27 5 is the common difference. an+1 = an + d

Sequences and Series.

Geometric Sequences and Series

Homework Check.

Section 2 – Geometric Sequences and Series

Geometric Sequence Skill 38.

Unit 5 – Series, Sequences, and Limits Section 5

Geometric Sequences and Series

Warm Up Write the first 4 terms of each sequence:

Section 12.3 Geometric Sequences; Geometric Series

Presentation transcript:

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

NOTE The difference between a series and a sequence is that a sequence is a list of terms, where a series is an indicated sum of the terms of sequence. In section 13.3 we will consider finite series and their sums.

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

Ex. Find S 50 of the arithmetic series… …

Formulas The sum of the first n terms of a geometric series is: Where r is the common ratio and r ≠ 1

Ex. Find the sum of …

Find the sum of all positive 3-digit integers that are divisible by 8. Example:

Example: Find the sum of the first 10 terms of the geometric series 2 – – 54 + …