Welcome Activity 1. Find the sum of the following sequence: 2 + 4 + 6 + 8 + 10 2. Find the number of terms (n) in the following sequence: 5, 9, 13, 17,

Slides:

Advertisements

Similar presentations

Arithmetic Series Vocabulary series: the sum of the indicated terms in a sequence arithmetic series: the sum of an arithmetic sequence.

Advertisements

Arithmetic Sequences (9.2)

9.2 Arithmetic Sequence and Partial Sum Common Difference Finite Sum.

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 13.3 The arithmetic sequence

Homework Questions.

Arithmetic and Geometric Series (11.5) Short cuts.

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

9/8/2015Math SL1 - Santowski1 Lesson 30 - Summation Notation & Infinite Geometric Series Math SL1 - Santowski.

2, 4, 6, 8, … a1, a2, a3, a4, … Arithmetic Sequences

Arithmetic Sequences and Series

6.1 Sequences and Arithmetic Sequences 3/20/2013.

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.

Notes 9.4 – Sequences and Series. I. Sequences A.) A progression of numbers in a pattern. 1.) FINITE – A set number of terms 2.) INFINITE – Continues.

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

Arithmetic Series. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, , 7, 11, 15,

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

1.1 Cont. Give the first 4 terms of the sequence: a. b. Warm-up (IN)

Aim: What is the summation notation?

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.

Warm Up: Section 2.11B Write a recursive routine for: (1). 6, 8, 10, 12,... (2). 1, 5, 9, 13,... Write an explicit formula for: (3). 10, 7, 4, 1,... (5).

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

Pg. 395/589 Homework Pg. 601#1, 3, 5, 7, 8, 21, 23, 26, 29, 33 #43x = 1#60see old notes #11, -1, 1, -1, …, -1#21, 3, 5, 7, …, 19 #32, 3/2, 4/3, 5/4, …,

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

Aim: What is the arithmetic series ? Do Now: Find the sum of each of the following sequences: a) b)

Essential Questions Series and Summation Notation

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.

Arithmetic Sequences Sequence is a list of numbers typically with a pattern. 2, 4, 6, 8, … The first term in a sequence is denoted as a 1, the second term.

Sequences & Series: Arithmetic, Geometric, Infinite!

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

8.2 – Arithmetic Sequences. A sequence is arithmetic if the difference between consecutive terms is constant Ex: 3, 7, 11, 15, … The formula for arithmetic.

Objectives Understand the difference between a finite and infinite series. Write and evaluate an arithmetic series

Algebra 2 Arithmetic Series. Algebra 2 Series – is the expression for the sum of the terms of a sequence.

Warm Up DNE Sums of Infinite Series.

Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the.

Ch. 8 – Sequences, Series, and Probability

©2001 by R. Villar All Rights Reserved

11.3 – Geometric Sequences and Series

13.3 – Arithmetic and Geometric Series and Their Sums

Geometric Sequences and Series (Section 8-3)

Review Write an explicit formula for the following sequences.

The symbol for summation is the Greek letter Sigma, S.

Series and Financial Applications

Bellwork Find the next two terms of each sequence.

7.5 Arithmetic Series.

Objectives Understand the difference between a finite and infinite series. Write and evaluate an arithmetic series.

Chapter 12 Section 2.

Warm-up: 1. For an arithmetic sequence, , find,

Chapter 12 – Sequences and Series

Sequences & Series.

Finite Geometric Series

DAY 30 AGENDA: Quiz Tues.

Definitions Series: an indicated sum of terms of a sequence

Geometric Sequences.

Chapter 12 Review Each point your team earns is extra points added to your score on the upcoming test.

DAY 31: Agenda Quiz minutes Thurs.

Warm Up Write an explicit formula for the following sequences.

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

Arithmetic Sequences Unit 6 Notes.

Activity 19 Review Algebra 2 Honors.

Note: Remove o from tonight’s hw

13.3 Arithmetic & Geometric Series

Chapter 1 Sequences and Series

Presentation transcript:

Welcome Activity 1. Find the sum of the following sequence: 2 + 4 + 6 + 8 + 10 2. Find the number of terms (n) in the following sequence: 5, 9, 13, 17, … 81, 85

HW Key

Summation Notation & Arithmetic Series Unit 1 Chapter 11 Summation Notation & Arithmetic Series

Objectives Students will be able to find the partial sum of an arithmetic series. HW: p. 780: 30, 32, 38, 50, 60

A series is formed when the terms of a sequence are added. In general, the sum of n terms in a finite series is written u1 + u2 + u3 + . . . + un = Sn The sum of an infinite series is written: u1 + u2 + u3 + . . . = S∞

This sum can be expressed using a shorthand notation: u1 + u2 + u3 + . . . + un = Sn = u1 + u2 + u3 + . . . = S∞ = Please note that i in this context does not refer to imaginary numbers.

Ex 1: Find the sum of the series.

Ex 2: Write the series in summation notation. 3 + 5 + 7 + 9 + 11 + 13

When the famous mathematician Karl Friedrich Gauss (1777-1855) was nine years old, his teacher asked the class to find the sum of the numbers from 1 to 100. Historical accounts indicate the teacher was hoping to take a break from his students and expected the students to add the terms one by one.

1 + 2 + 3 + . . . + 98 + 99 + 100 = S100 100 + 99 + 98 + . . . + 3 + 2 + 1 = S100 101 + 101 + 101 + . . . + 101 + 101 + 101 = 2 (S100)

Gauss’ creative thinking can be used to derive the explicit formula for the sum of an arithmetic series: u1 + u2 + u3 + . . . + u n - 2 + u n - 1 + u n = Sn u n + u n - 1 + u n - 2 + . . . + u3 + u2 + u1 = Sn (u1 + u n ) · n = 2 (Sn)

Explicit Formula for the sum of an arithmetic series: where n is the number of terms, u1 is the first term, and un is the last term.

Ex 3: Find the sum of the first 10 terms given: a3 = 5 and a4 = 8.

Ex 4: Find the sum of the first 50 multiples of 6.

Ex 5: Find a1 and d given S20 = 1090 and a20 = 102

Ex 6: Find the sum of the arithmetic series: 89 + 84 + 79 + 74 + . . . + 9 + 4

Ex 7: Evaluate the sum: