K12MATH011: Algebra II

Unit 9: Sequences and Series   In this final unit, you will be introduced to sequences and series. A sequence is a function defined over the positive integers. A series is a sequence in which the terms are summed. For general functions, the domain may be any subset of the real or complex numbers, but sequences are restricted to counting numbers. Sequences are often used to mimic functions in complex processes and are often used in mathematical modeling and analysis.

Unit 9 Time Advisory
Completing this unit should take approximately 10 hours and 30 minutes.

☐    Subunit 9.1: 1 hour and 15 minutes

☐    Subunit 9.2: 3 hours and 15 minutes

☐    Subunit 9.3: 2 hours 

☐    Subunit 9.4: 45 minutes

☐    Subunit 9.5: 3 hours and 15 minutes

Unit9 Learning Outcomes
Upon successful completion of this unit, you will be able to: - Find the nth term of any sequence, given the first four or five terms. - Find the nth term of an arithmetic sequence. - Find the nth term of a geometric sequence. - Find the sum of a finite geometric sequence using the sum formula.

Standards Addressed (Common Core): - CCSS.Math.Content.HSF-IF.A.3 - CCSS.Math.Content.HSF-BF.A.2 - CCSS.Math.Content.HSF-LE.A.2  - CCSS.ELA-Literacy.RST.9-10.1 - CCSS.ELA-Literacy.RST.9-10.5 - CCSS.ELA-Literacy.WHST.11-12.1 - CCSS.ELA-Literacy.WHST.11-12.2

9.1 Definition of Sequences and Series   Sequences are progressions of numbers that may be random but most often are formed by patterns. They are useful in that they may be used in programming to mimic certain functions, to which they are closely related.

9.2 Arithmetic Sequences   These are sequences formed by starting with a value and adding the same fixed number over and over again. These sequences are related to and may be substituted for linear functions.

9.3 Geometric Sequences   In geometric sequences, each term is found by taking a starting value and multiplying it repeatedly by a fixed, nonzero number. These sequences are among the most commonly used in mathematics, and they are related to and may substitute for exponential functions.

9.4 The Fibonacci Sequence   The Fibonacci sequence was named for Leonardo of Pisa, called Fibonacci, who first studied the pattern. The Fibonnaci sequence begins with 0 and 1. Then the sequence is generated by adding consecutive numbers to get the next term. Applications can be found in the fields of art, engineering, botany, computer programming, and business.

9.5 The Sum Formula   The sum of terms of a sequence is called a series. Such sums can almost always be patterned into a formula, provided the sequence is not merely a random set of numbers. This is one example, using the sum of arithmetic sequences, which can most definitely be used to create a formula.

Final Exam   - Final Exam: The Saylor Foundation's “K12MATH011 Final Exam” Link: The Saylor Foundation's “K12MATH011 Final Exam” (HTML)
Instructions: You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.