UNIT 1 - ARITHMETIC & GEOMETRIC SEQUENCES
Task #7 – Michigan Stadium Problem (Arithmetic Series)
Common Core: HS.A-SSE.4, HS.F-BF.1, 2
MA40: ALGEBRA 2
Name:
Period:
INVESTIGATION
Michigan Stadium Problem: The University of Michigan Stadium is the
largest football stadium in the United States. You are responsible for
selling concessions to a section of the stadium. Each row in the section
has 4 more seats than the row in front of it. The first row of your section
has 35 seats. If everyone in row 5 orders a hot dog, how many hot dogs
do you need to bring? If everyone in row 92 orders popcorn, how much
popcorn do you need to bring? How many total seats are you responsible
for in your section if your section has 96 rows?
1.
Sketch a series of pictures that illustrates what is happening in this
problem. Then, using words, describe the situation.
Pictures:
Words:
2.
Complete the table. Explain your method for completing the table.
Row
Number
1
2
Number of
Seats
Table Scratch Work:
Explanation:
3
4
5
…
...
92
93
94
95
96
Unit 1.7 – Michigan Stadium Problem (Arithmetic Series) – (continued)
3.
How many hot dogs did you need for row 5? _______________
How much popcorn did you need for row 92? _______________
4.
How many total seats are there in your section? _______________
Describe how you came up with this number. If you could not come up
with a number, describe the problem as you see it. Use pictures,
tables, graphs, etc.
5.
Class Discussion – Let’s discuss how we can determine the total
number of seats in your section.
Unit 1.7 – Michigan Stadium Problem (Arithmetic Series) – (continued)
DEVELOPING MATH CONCEPTS & TERMS
Arithmetic Series – The expression formed by adding the terms of an
arithmetic sequence.
6.
Decide whether the following is an arithmetic series.
a)  3,  6,  9,  12,  15, ...
b)
c) 7  0  7  14  21  ...
d)
2  4  8  16  32
15
 3i  1
i 1
1
2 

3
n 1
25
e)
n 1

f)
 2k
k 1
Sum of a Finite Arithmetic Series
The sum of the first n terms of an arithmetic series is:
In words, S n is the mean of the first and nth terms, multiplied by the
number of terms.
7.
Find the sum of the first 30 terms of the series 3 
7
9
 4   5  ...
2
2
Unit 1.7 – Michigan Stadium Problem (Arithmetic Series) – (continued)
11
8.
Find the sum of the series
 4n  1 .
n 3
9.
Find the sum of the arithmetic series 6  13  20  27  ...  97.
10. Logs are stacked in a pile. The bottom row has 21 logs and the top row
has 15 logs. Each row has one less log than the row below it. How
many logs are in the pile?
Summary: