Series: Sequences and Series
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About this Series
- Lessons: 5
- Total Time: 6h 20m
- Use: Watch Online
- Access Period: 90 Days
- Created At: 08/05/2009
- Last Updated At: 05/17/2013
this series of 5 Lessons will teach you arithmetiic sequences and series, goemetric sequences and series and the summation notation (sigma) notation for a series.
These lessons will teach you how to find the:
- first term
- common difference
- number of terms
- arithmetic & geometric means
- common ratio
- specific term
- number of terms to be summed
and, to:
- use the last term formula
- use a system of equations to solve problems
- insert geometric means
- determine if a series is arithmetic or geometric
- write the series given the general term
write the terms of arithmetic & geometric series in summation (sigma) notation
About this Author
-
- Teacher Sydney
- 57 lessons
- Joined:
07/02/2009
Teacher Sydney is a certified teacher, B.A., B. Ed. (Math Major) with 30+ years experience teaching Math to High School and Continuing Education students. She developed these very comprehensive, detailed audio visual math tutorials to help those who were serious about learning math. Her success stories with students are numerous, from students who said to her "I never understood math until your classes" to adult students who went on to successful careers, one providing feedback "Your adult ed classes enabled me to meet university entrance requirements and, ... I am now an Engineer, thank you!". She had a reputation for teaching the math class that “you want to be in.” For more...
Lessons Included
Below are the descriptions for each of the lessons included in the series:
-
Sequences: Arithmetic Sequences 450
This 74 minute sequences & series lesson begins with the terminology of a sequence and will show you how to use the general term formula to find any term of an arithmetic sequence as well as:
- find the first term
- find common difference
- find number of terms
- find & insert arithmetic means
- determine if the series is finite or infiniteExample Question: If x + 4, 3x, x^2 are the first three terms in an arithmetic sequence, find the sequence.
This lesson contains explanations of the concepts and 20 example questions with step by step solutions plus 7 interactive review questions with solutions.
Lessons that will help you with the fundamentals of this lesson include:
- 105 Rules for Integers and Absolute Value (http://www.mindbites.com/lesson/5073)
- 110 Basic Algebra Part I (http://www.mindbites.com/lesson/5060)
- 135 Solving Linear Equations Part I (http://www.mindbites.com/lesson/5068)
- 205 Solving Systems of Linear Equations (http://www.mindbites.com/lesson/5083)
- 230 Solving Quadratic Equations by Factoring (http://www.mindbites.com/lesson/5087) -
Series: Arithmetic Series 455
This 68 minute sequences & series lesson begins with the terminology of a series and will show you how to use the general sum formula to find the sum of an arithmetic series as well as how to:
- tell the difference between an arithmetic sequence and an arithmetic series
- find the first term
- find the common difference
- find the number of terms
- use the last term formula
- use a system of equations to solve problemsSample question: A movie theatre has 40 rows of seats. Each row has three more seats than the previous row. If there are a total of 4140 seats in the theatre, how many seats are there in the first row?
This lesson contains explanations of the concepts and 15 example questions with step by step solutions plus 7 interactive review questions with solutions.
Lessons that will help you with the fundamentals of this lesson include:
- 105 Rules for Integers and Absolute Value (http://www.mindbites.com/lesson/5073)
- 110 Basic Algebra Part I (http://www.mindbites.com/lesson/5060)
- 135 Solving Linear Equations Part I (http://www.mindbites.com/lesson/5068)
- 205 Solving Systems of Linear Equations (http://www.mindbites.com/lesson/5083)
- 230 Solving Quadratic Equations by Factoring (http://www.mindbites.com/lesson/5087)
- 450 Arithmetic Sequences (http://www.mindbites.com/lesson/5113) -
Sequences: Geometric Sequences 460
This 78 minute sequences & series lesson will show you how to use the general term formula to find any term in a geometric sequence as well as how to:
- identify a geometric sequence
- find the common ratio, the first term, the number of terms
- find and insert geometric means
- find a specific term
- use a system of equations to solve problemsSample question: Insert 3 geometric means between 8 and 1/2.
This lesson contains explanations of the concepts and 20 example questions with step by step solutions plus 7 interactive review questions with solutions.
Lessons that will help you with the fundamentals of this lesson include:
- 085 Fractions (http://www.mindbites.com/lesson/5074)
- 115 The 5 Basic Exponent Laws (http://www.mindbites.com/lesson/5061)
- 160 Operations With Radicals (http://www.mindbites.com/lesson/5065)
- 165 The zero, Negative and Rational Exponents (http://www.mindbites.com/lesson/5069)
- 230 Solving Quadratic Equations by Factoring (http://www.mindbites.com/lesson/5087) -
Series: Geometric Series 465
This 85 minute sequences & series lesson will show you how to use the general sum formula to find the nth partial sum of a geometric series as well as how to:
- tell the difference between a geometric sequence and a geometric series
- find the first term
- the common ratio
- the number of terms
- use the last term formula
- use a system of equations to solve problemsSample question: You have 2 parents, 4 grandparents, 8 great grandparents, etc. How many ancestors are their in 12 generations of your family?
This lesson contains explanations of the concepts and 17 example questions with step by step solutions plus 7 interactive review questions with solutions.
Lessons that will help you with the fundamentals of this lesson include:
- 115 The 5 Basic Exponent Laws (http://www.mindbites.com/lesson/5061)
- 230 Solving Quadratic Equations by Factoring (http://www.mindbites.com/lesson/5087)
- 460 Geometric Sequences (http://www.mindbites.com/lesson/5117) -
Sequences & Series: Summation (Sigma) Notation 470
This 73 minute sequences & series lesson will show you how to use the summation (sigma) notation, index, lower limit, upper limit and to write the terms of a series as well as how to:
- determine if a series is arithmetic or geometric
- find the number of terms to be summed in a series written in the summation (sigma) notation
- write the series when given the general term
- write the terms of arithmetic and geometric series in summation (sigma) notation
- simplify arithmetic and geometric series expressed in summation, (sigma) notationSample question: Write the series using summation (sigma) notation and then find the sum: -13 -17 -21 ... -173
This lesson contains explanations of the concepts and 18 example questions with step by step solutions plus 7 interactive review questions with solutions.
Lessons that will help you with the fundamentals of this lesson include:
- 115 The 5 Basic Exponent Laws (http://www.mindbites.com/lesson/5061)
- 455 Arithmetic Series (http://www.mindbites.com/lesson/5116)
- 465 Geometric Series (http://www.mindbites.com/lesson/5106)
Supplementary Files:
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All the instruction in this lesson was great, no complaints. The instructor's voice is just so monotone that I have a hard time staying engaged through the entire lesson. Just a small complaint, other than that it is great.