# AII.5 - Sequences and Series

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.

### 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

2016 VDOE Curriculum Framework - AII.5 Understanding

·  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

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

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

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

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

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

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

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

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

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

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

·  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.

·  AII.56  Given the formula, determine the sum of a convergent infinite 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: Aug 23, 2018