#### Math - 2017-18

# 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 *n*^{th} term, and
evaluating summation formulas. Notation will include Σ and *a _{n}*.

AII.5The 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 n^{th}term, and evaluating summation formulas. Notation will include Σ and a_{n}.

**Bloom's Level:** Analyze, Apply

*Adopted: 2009*

### 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.2_{3} **Use**
and **interpret** the notations ∑,
*n*, *n*^{th} term, and *a*_{n}.

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

All.2_{7} **Model** real-world situations using
sequences and series.

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

__Sequences (Arithmetic &
Geometric)__

All.2_{1} **Distinguish**
between a sequence and a series

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

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

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

All.2_{3} **Use**
and **interpret** the notations ∑,
*n*, *n*^{th} term, and *a*_{n}.

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

All.2_{4} Given the formula, **find** (the nth term) for an arithmetic
or geometric sequence.

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

*n*

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

All.2_{7} **Model** real-world situations using
sequences and series.

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

__Series (Arithmetic &
Geometric)__

All.2_{1} **Distinguish**
between a sequence and a series

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

All.2_{3} **Use**
and **interpret** the notations ∑,
*n*, *n*^{th} term, and *a*_{n}.

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

All.2_{5} Given formulas, **write** the first n terms and **find**
the sum, , of the first n terms of an arithmetic or a
geometric sequence.

·
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.

All.2_{6} Given the formula, **find** the sum of a convergent infinite series.

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

All.2_{7} **Model** real-world situations using
sequences and 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: Oct 27, 2017*