Algebra 2 Online!
Henrico County Public Schools, Virginia
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AII.2a
The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and evaluating summation formulas. Notation will include S and an.
*Standard AII.2 will be assessed in the Functions and Statistics reporting category. (Revised March 2011)
 Essential Knowledge and Skills Distinguish between a sequence and a series. Generalize patterns in a sequence using explicit and recursive formulas. Use and interpret the notations å, n, nth term, and an. Given the formula, find an (the nth term) for an arithmetic or a geometric sequence. Given formulas, write the first n terms and find the sum, Sn, of the first n terms of an arithmetic or geometric series. Given the formula, find the sum of a convergent infinite series. Model real-world situations using sequences and series. Essential Understandings Sequences and series arise from real-world situations. The study of sequences and series is an application of  the investigation of patterns. A sequence is a function whose domain is the set of natural numbers. Sequences can be defined explicitly and recursively.
Vertical Articulation
1. SOL 7.2 - describe/represent arithmetic/geometric sequences using variable expressions
Instructional Materials
1. VDOE ESS Lesson: Arithmetic and Geometric Sequences and Series - Expressions and Operations (PDF) - Exploring sequences and series (Word)
Real World Lessons
1. Incredible Shrinking Dollar - What will the dollar bill look like after getting reduced that many times?
Practice
Self-Assessments
Skills
1. Mathematics Assessment Project
• A06:Sidewalk Patterns - Apprentice - In Prague some sidewalks are made of small square blocks of stone. The blocks are in different shades to make patterns that are in various sizes. In this task, you will look for rules which let you work out how many blocks of different colors are needed to make different sized patterns. (This task is very similar to Sidewalk Stones, but offers more step-by-step guidance.)
• A20:Multiplying Cells - Apprentice - Students in a science lab observe cells multiplying. Your task is to use their observation to work out how the number of cells increases over time.
• E13:Sidewalk Stones - Expert - This task is very similar to Sidewalk Patterns, but offers less step-by-step guidance.
2. JMU Pivotal Question: Arithmetic and Geometric Sequences (doc)
Videos
1. Video Tutor - Arithmetic Sequences
2. Video Tutor - Geometris Sequences
Explore Learning
1. Arithmetic Sequences - Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response.
2. Geometric Sequences - Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas.
3. Arithmetic and Geometric Sequences - Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.
Websites
1. Notes: Arithmetic Series and Sequences notes
2. Notes: Geometric Series and Sequences notes
Common Core Standards
 N-RN.2 A-SSE.4 F-IF.3 F-BF.2 F-LE.2