Algebra 2 Applications Lesson Plan Outline
Lesson Title: Geometric Series Lesson 4
Washington State Algebra 2 Standard Name(s) and Number(s):
A2.7.C Find the terms and partial sums of arithmetic and geometric series and the infinite
sum for geometric series.
Learning objective:
Students will learn what Geometric series is, derive and use the formula to find the sum of a
geometric series.
Prerequisite Skills:
Evaluating expressions, understanding of geometric sequences.
Material for Students:
Small white boards if available
Teaching Aids:
Estimated Time For Completion:
References:
I.
PREASSESSMENT:
a. Giving students a simple sequence with missing terms
b. The term common ratio
II.
INTRODUCTION:
Class opener: Junk mail madness!
Gru, one of the world’s worst villains wants to prove that HE is the worst villain of all. His
plan is to disable as many computers in the world as possible. He has created a virus which
will forward his mail to three other accounts on the address book of the receiver and also
wipe out the hard drive on the computer. (This virus cannot be detected by any anti-virus
scans.) This process will continue until everyone receives his message. Gru sent out this
message today, how many people will be impacted after 3 days? After 5 days? Assuming
there are about 1.5 billion accounts out there, how long will it take for Everyone to get his
e-mail?
a. Pair: Students work in pairs to come up with different strategies to solve the
problem.
b. Class: Discuss different strategies that the students use to find the sum. The last
part of the question can be discussed in the application section.
III.
LESSON:
Use 1+2+4+8+16+32… to derive the formula.
Find the sum for the first 8 terms.
𝑆8 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128
Since the common ratio is 2, multiply all terms by 2
2𝑆8 = 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256
Align the two equations on top of each other. Discuss with students what we can do with
these two equations to find the sum for the first 8 terms.
𝑆8 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128
(−)2𝑆8 =
2 + 4 + 8 + 16 + 32 + 64 + 128 + 256
(1 − 2)𝑆8 = 1 − 256
1 − 256 −255
𝑆8 =
=
= 255
1−2
−1
Ok this is great that we found the sum for this geometric series, what can we generate for other
geometric series without having to go through this process again?
Last term in series
multiply by common
ratio
First term in series
𝑆8 =
1 − 256
1−2
Common ratio
𝑺𝑺 𝑺𝒏 =
IV.
𝒂𝟏 − 𝒂𝟏 𝒓𝒏
𝒂𝟏 − 𝒓
APPLICATION
Back to the class opener, Junk mail madness. How many days will it take to send out about
1.5 billion junk mail?
1 − 3𝑛
1500000000 =
1−3
𝑛 ≈ 19.86 days
Practices such as finding the sum using the formula can be found in Algebra II textbooks.
V.
ASSESSMENT
a. Exit slip: Describe geometric sequences and series in your own word. Think of a way
that would help you remember geometric sequences and series.
VI.
EXTENSIONS
a. Sigma notation, what is it? How is it used to find the sum of geometric series?
b. Why is Sigma notation a useful way to write a series
c. Compare and contrast Arithmetic and Geometric sequences (possibly in Venn
diagram)
Arithmetic Sequence
Differences
Geometric Sequence
Differences
d. Discuss infinite sum of a geometric series. What does it mean? How will you find
the sum? In what context will see infinite sum of a geometric series?
Based on: CURRICULUM GUIDE FOR PROFESSIONAL TECHNICAL COLLEGE INSTRUCTORS
TEACHING & FACILITATING LEARNING - LEVEL I