Sequences and Series

This week's topic is one usually studied in first year algebra: sequences and series. Let's start with some definitions. A sequence is an ordered list of numbers, and a series is the sum of the terms (the individual numbers) of a sequence. For more lessons, here are my weekly website picks.

• Cool Math Algebra: Sequences & Series Lessons5 stars

"A sequence is a list of numbers (or other things) that changes according to some sort of pattern." This ten lesson section introduces arithmetic sequences, series, sigma notation, geometric sequences, mathematical induction and the binomial theorem. To move from one lesson to the next (each lesson is multiple pages), you need to return to this menu, which is linked at the bottom of each page.

• Math is Fun: Arithmetic Sequences – Finding a Rule5 stars

"To find a missing number, first find a Rule behind the Sequence. Sometimes you can just look at the numbers and see a pattern." After a few examples of how trial and error can help you discover a rule, at the bottom of the page you'll find links to related topics, including Arithmetic Sequences, Geometric Sequences, Fibonacci Sequence and Triangular Sequence. Each of these topics also include related links at the bottom of the page, so be sure to look for them.

• Math Guide: Arithmetic Sequences5 stars

After defining arithmetic sequences, this Math Guide lesson explains how to calculate the nth term. "In order for us to know how to obtain terms that are far down these lists of numbers, we need to develop a formula that can be used to calculate these terms. If we were to try and find the 20th term, or worse to 2000th term, it would take a long time if we were to simply add a number -- one at a time -- to find our terms." At the bottom of the page, you'll find four interactive quizzes on sequences and series.

• Regents Prep: Arithmetic Sequences and Series5 stars

"While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences." This one-page lesson explains arithmetic sequences with lots of examples. At the bottom of the page is a link to a lesson about using a TI-83+/84+ graphing calculator for sequences and series. Very cool.

• Virtual Math Lab: College Algebra: Arithmetic Sequences and Series5 stars

"Be careful that you don't think that every sequence that has a pattern in addition is arithmetic. It is arithmetic if you are always adding the SAME number each time." This one-page lesson with practice problems is just one of three tutorials on the topic of sequences and series at the Virtual Math Lab. You'll find the others linked both in the introductory paragraph, and interspersed in the lesson itself. The practice problems at the bottom of the page are meant to be worked out on your own before clicking through to the answer/discussion page.

• By . Originally written on Apr 02, 2013. Last Modified on Apr 03, 2013.

• Honorable Mentions

The following links are either new discoveries or sites that didn't make it into my newspaper column because of space constraints. Enjoy!

• Purple Math: Sequences and Series

•  Growing Patterns: Fibonacci Numbers in Nature by Sarah C. Campbell (Hardcover) - Usually ships in 24 hours Price: \$10.09
 What Happens Next? Picture Sequencing Board Game: 3-scene puzzles from Carson-Dellosa Publishing (Game) - Usually ships in 24 hours Price: \$8.26
 What's Next, Nina? (Math Matters (Kane Press Paperback)) by Sue Kassirer (Paperback) - Usually ships in 24 hours Price: \$0.01