# AII.2 and *AII.5 - Sequences and Series

AII.2    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 Σ and an.

AII.5  The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, determining the nth term, and evaluating summation formulas. Notation will include Σ and an.

Bloom's Level:  Analyze, Apply

### BIG IDEAS

• I can crack a secret code, figure compound interest, and determine a retirement salary if given the same raise each year.
• I will recognize that patterns exhibit relationships that can be extended, described, and generalized.

### UNDERSTANDING THE STANDARD

• 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.

·  Sequences and series arise from practical 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.

### ESSENTIALS

Introduction

All.23  Use and interpret the notations ∑, n, nth term, and an.

·  AII.53  Use and interpret the notations å, n, nth term, and an.

All.27  Model real-world situations using sequences and series.

·  AII.57  Model practical situations using sequences and series.

Sequences (Arithmetic & Geometric)

All.21  Distinguish between a sequence and a series

·  AII.51  Distinguish between a sequence and a series.

All.22  Generalize patterns in a sequence using explicit and recursive formulas.

·  AII.52  Generalize patterns in a sequence using explicit and recursive formulas.

All.23  Use and interpret the notations ∑, n, nth term, and an.

·  AII.53  Use and interpret the notations å, n, nth term, and an.

All.24  Given the formula, find  (the nth term) for an arithmetic or geometric sequence.

·  AII.54  Given the formula, determine an (the nth term) for an arithmetic or a geometric sequence.

All.27  Model real-world situations using sequences and series.

·  AII.57  Model practical situations using sequences and series.

Series (Arithmetic & Geometric)

All.21  Distinguish between a sequence and a series

·  AII.51  Distinguish between a sequence and a series.

All.23  Use and interpret the notations ∑, n, nth term, and an.

·  AII.53  Use and interpret the notations å, n, nth term, and an.

All.25  Given formulas, write the first n terms and find the sum, , of the first n terms of an arithmetic or a geometric sequence.

·  AII.55  Given formulas, write the first n terms and determine the sum, Sn, of the first n terms of an arithmetic or geometric series.

All.26  Given the formula, find the sum of a convergent infinite series.

·  AII.56  Given the formula, determine the sum of a convergent infinite series.

All.27  Model real-world situations using sequences and series.

·    AII.57  Model practical situations using sequences and series.

### KEY VOCABULARY

sequence, series, arithmetic sequence, arithmetic series, geometric sequence, geometric series, summation, ∑, an, nth, Sn, explicit, recursive, convergent infinite series

Updated: Oct 27, 2017