Key Concepts
Sequences and Their Notations Arithmetic Sequences Geometric Sequences Series and Their Notations Counting Principles Binomial Theorem Probability
Probability
Learning Objectives In this section, you will: Figure 1 An example of a “spaghetti model,” which can be used to predict possible paths of a tropical storm.1 Residents of the Southeastern United States are all too familiar with charts, known as spaghetti…
Binomial Theorem
Learning Objectives In this section, you will: A polynomial with two terms is called a binomial. We have already learned to multiply binomials and to raise binomials to powers, but raising a binomial to a high power can be tedious…
Counting Principles
Learning Objectives In this section, you will: A new company sells customizable cases for tablets and smartphones. Each case comes in a variety of colors and can be personalized for an additional fee with images or a monogram. A customer…
Series and Their Notations
Learning Objectives In this section, you will: A parent decides to start a college fund for their daughter. They plan to invest $50 in the fund each month. The fund pays 6% annual interest, compounded monthly. How much money will…
Geometric Sequences
Learning Objectives In this section, you will: Many jobs offer an annual cost-of-living increase to keep salaries consistent with inflation. Suppose, for example, a recent college graduate finds a position as a sales manager earning an annual salary of $26,000.…
Arithmetic Sequences
Learning Objectives In this section, you will: Companies often make large purchases, such as computers and vehicles, for business use. The book-value of these supplies decreases each year for tax purposes. This decrease in value is called depreciation. One method…
Sequences and Their Notations
Learning Objectives In this section, you will: A video game company launches an exciting new advertising campaign. They predict the number of online visits to their website, or hits, will double each day. The model they are using shows 2…
Introduction to Sequences, Probability and Counting Theory
(credit: Robert Couse-Baker, Flickr.) Chapter Outline 13.1 Sequences and Their Notations 13.2 Arithmetic Sequences 13.3 Geometric Sequences 13.4 Series and Their Notations 13.5 Counting Principles 13.6 Binomial Theorem 13.7 Probability A lottery winner has some big decisions to make regarding what to do with the winnings. Buy…
Key Concepts
The Ellipse The Hyperbola The Parabola Rotation of Axes Conic Sections in Polar Coordinates