#### Math - 2019-20

# AII.5 - Sequences and Series

AII.5The student willinvestigateandapplythe properties of arithmetic and geometric sequences and series tosolvepractical problems, includingwritingthe first n terms,determiningthe n^{th}term, andevaluatingsummation formulas. Notation will include Σ and a_{n}.

*Adopted: 2016*

### 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 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.5_{3} **Use**
and **interpret** the notations å,* n*, *n*^{th }term,
and *a _{n}*.

·
AII.5_{7} **Model**
practical situations using sequences and series.

·
AII.5_{1} **Distinguish**
between a sequence and a series.

·
AII.5_{2} **Generalize**
patterns in a sequence using explicit and recursive formulas.

·
AII.5_{3} **Use**
and **interpret** the notations å,* n*, *n*^{th }term,
and *a _{n}*.

·
AII.5_{4} Given the formula, **determine** *a _{n}*
(the

*n*

^{th}term) for an arithmetic or a geometric sequence.

·
AII.5_{7} **Model**
practical situations using sequences and series.

·
AII.5_{1} **Distinguish**
between a sequence and a series.

·
AII.5_{3} **Use**
and **interpret** the notations å,* n*, *n*^{th }term,
and *a _{n}*.

·
AII.5_{5} Given formulas, **write** the first *n* terms
and **determine** the sum, *S _{n}*

_{, }of the first

*n*terms of an arithmetic or geometric series.

·
AII.5_{6} Given the formula, **determine** the sum of a convergent infinite series.

·
AII.5_{7}
**Model** practical situations
using sequences and series.

### KEY VOCABULARY

sequence,
series, arithmetic sequence, arithmetic series, geometric sequence, geometric
series, summation, ∑, a_{n}, n^{th}, S_{n}, explicit,
recursive, convergent infinite series

*Updated: Aug 23, 2018*