CMS Curriculum Guide 2011-2012
Advanced Functions & Modeling
Unit Title: Sequences & Series
suggested time: 10 days
Enduring understanding (Big Idea):
Sequences and series can be used to predict patterns. For example, arithmetic sequences can be used to determine
the number of band members in a specified row of a pyramid formation.
Essential Questions:
 What types of patterns can be modeled mathematically?
 How can recognizing patterns help you solve real-world problems?
Recommended
Days
Textbook Alignment
10-1 Sequences,
Series, and Sigma
Notation
2 days
10-2 Arithmetic
Sequences and series
2 days
10-3 Geometric
Sequences and series
2 days
10-5 The Binomial
Theorem
1 day
Mathematical Objectives
Connections to 2003 Standards
 Investigate several different
types of sequences
 Use sigma notation to represent
and calculate sums of sequences
2.05 Use recursively-defined functions to
model and solve problems.
 Find the nth terms and
arithmetic means of arithmetic
sequences
 Find sums of n terms of
arithmetic series
a. Find the sum of a finite sequence.
c. Determine whether a given series
converges or diverges.
d. Translate between recursive and explicit
representations
2.05 Use recursively-defined functions to
model and solve problems.
a. Find the sum of a finite sequence.
c. Determine whether a given series
converges or diverges.
 Find the nth terms and
geometric means of arithmetic
geometric
 Find sums of n terms of
geometric series
 Find the sums of infinite
geometric series
2.05 Use recursively-defined functions to
model and solve problems.
 Use Pascal’s Triangle to write
binomial expansions
 Use the Binomial Theorem to
write and find the coefficients of
specified terms in binomial
expansions
1.03 Use theoretical and experimental
probability to model and solve problems.
a. Find the sum of a finite sequence.
b.Find the sum of an infinite sequence.
c. Determine whether a given series
converges or diverges
f. Apply the Binomial Theorem.
CMS Curriculum Guide 2011-2012
Advanced Functions & Modeling
Vocabulary:
sequence
term
finite sequence
infinite sequence
recursive sequence
explicit sequence
Fibonacci sequence
converge
diverge
series
finite series
nth partial sum
infinite series
sigma notation
Resources:
Glencoe McGraw-Hill (TE) Precalculus
Teacher Works Plus Precalculus
Formal Assessments:
 Quizzes
 Review Quiz (Practice Test)
 Unit Test
connected.mcgraw-hill.com
arithmetic sequence
common difference
arithmetic means
first difference
second difference
arithmetic series
geometric sequence
common ratio
geometric means
geometric series
power series
exponential series
Euler’s formula