Inferences and Conclusions from Data Assignment

Please complete the following questions. It is important that youshow all work you did to solve the problems when you submit your work.This includes any calculations, diagrams, or graphs that helped yousolve it.

Writing in Math Use the information onpage 649 to explain how arithmetic series apply to amphitheaters.Explain what the sequence and the series that can be formed from thegiven numbers represent, and show two ways to find the seating capacityof the amphitheater if it has ten rows of seats. Page 649 is in the attatchments. Writing in Math Use the information onpage 663 to explain how e-mailing a joke is related to a geometricseries. Include an explanation of how the situation could be changed tomake it better to use a formula than to add terms. Page 663 is in the attachments 545649/1100
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American
High School
• Find sums of
arithmetic series
– Use sipna notation
New Vocabulary
eries
rithmetic series
ma notation
dex of summation
Austin, Texas has a strong musical
tradition. It is home to many indoor and
outdoor music venues where new and
established musicians perform regularly.
Some of these venues are amphitheaters
that generally get wider as the distance
from the stage increases.
Suppose a section of an amphitheater can
seat 18 people in the first row and each
row can seat 4 more people than the
previous row.
Gaga
Arithmetic Series The numbers of seats in the rows of the amphitheater
form an arithmetic sequence. To find the number of people who could sit
in the first four rows, add the first four terms of the sequence. That sum
is 18 + 22 + 26 + 30 or 96. A series is an indicated sum of the terms of a
sequence. Since 18, 22, 26, 30 is an arithmetic sequence, 18 + 22 + 26 + 30
is an arithmetic series.
S represents the sum of the first n terms of a series. For example, 5, is the
sum of the first four terms.
tuly
649
adicat
e sum of a series is
e result when the
ms of the series are
Hed. An indicated
is the expression
tillustrates the
es which includes
To develop a formula for the sum of any arithmetic series, consider the
series below.
S, = 4 + 11 + 18 + 25 + 32 +39 +46 +53 + 60
Suppose you e-mail a joke to three friends on Monday. Each of those
friends sends the joke on to three of their friends on Tuesday. Each
person who receives the joke on Tuesday sends it to three more people
on Wednesday, and so on.
ans of
ary
E-Mail Jokes
OEX
Wander
Tende
О… …
….
III
Page
663
Geometric Series Notice that every day, the number of people who read
your joke is three times the number that read it the day before. By
Sunday, the number of people, including yourself, who have read the
joke is 1 + 3 + 9 + 27 +81 +243 + 729 + 2187, or 3280!
The numbers 1, 3,9, 27, 81, 243,729, and 2187 form a geometric sequence
in which a = 1 and r = 3. The indicated sum of the numbers in the
sequence, 1 + 3 + 9 + 27 +81 +243 + 729 + 2187, is called a
geometric series.