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Sequences and Series

Site: REMC 8 / Kent ISD Moodle VLE
Course: Algebra II - Staublin
Book: Sequences and Series
Printed by: Guest user
Date: Saturday, May 18, 2024, 3:37 PM

Table of contents

Number Patterns

Can you figure out the number patterns?  Try this activity then explore mathematical patterns and learn the difference between Recursive Series and Explicit Series in the videos below.

Assignment

  • Textbook 11-1: 1-9, 13-23 odds, 32, 42-43, 48, 51, 60

Resources

Videos

Arithmetic Sequences

Try this challenge problem: write a recursive formula for the Fibonacci Sequence. Then learn to write recursive and explicit formulas for arithmetic sequences from the videos below. Don't skip the video on Arithmetic Mean, you'll need to know that, too!

Assignment

  • Textbook 11-2: 3-69 (multiples of 3), 71

Resources

Videos

Geometric Sequences

Learn to write recursive and explicit formulas for Geometric Sequences from the videos below. Don't skip the video on Geometric Mean, you'll need to know that, too!

Assignment

  • Textbook 11-3: 2-40 evens, 48-52 evens

Resources

Videos

Sequences vs. Series

What's the difference between a Sequence and a Series?  Watch the video to find out.

Assignment

  • Textbook 11-4: 25-30

Resources

Summation Notation and Evaluating Series

Now that you know about sequences (an ordered set of numbers) and series (a sequence of numbers added all together), it's time to learn how to use summation notation to represent a finite series, and how to evaluate a finite series.

Assignment

  • Textbook 11-4: 13-18

Resources

Videos

Shortcut to Evaluate Finite Arithmetic Series

Evaluating a series can be lots of work, LOTS of tedious work!  Luckily for us, there's a shortcut for evaluating an arithmetic series. Watch the video, do the assignment.

Assignment

  • Textbook 11-4: 19-24
  • Textbook 11-4: For problems 1-2 and 35-37: write an explicit function for the series, write the series in Summation Notation, then evaluate the series using the Arithmetic Series shortcut.

Resources

Videos

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Shortcut to Evaluate Finite Geometric Series

Evaluating a series can be lots of work, LOTS of tedious work!  Luckily for us, there's a shortcut for evaluating a geometric series. Watch the video, do the assignment.

Assignment

  • Textbook 11-5: For problems 1-4, 5, 8: write an explicit function for the series, write the series in Summation Notation, then evaluate the series using the Geometric Series shortcut.

Resources

Videos

Infinite Arithmetic Series

Video forthcoming.

[spoiler: ALL infinite arithmetic series diverge.]

Check this out. Is it even possible?

Infinite Geometric Series

Weird things happen when we try to evaluate an infinite geometric series. Watch the videos, check it out. (Hint: look for divergence versus convergence!)

Assignment

  • Textbook 11-5: for problems 32-36, determine whether the series converges or diverges; if the series converges, find the sum on which it converges.

Resources

Videos

Area under a curve

Workshop

  • Area Under a Curve


Assignment

  • Textbook 11-6: 1-5, 7-11, 18-23


Resources

Review #1

Click the link to go to a set of review problems (with answers) about sequences and series.