The document discusses using a sequence to model the number of seats in rows of a movie theater. It provides: 1) The sequence formula Cn = 16 + 4n to calculate the number of seats in the nth row. 2) The numbers of seats in the first 5 rows as: 20, 24, 28, 32, 36. 3) That the last (50th) row will have 216 seats. 4) That the total number of seats in the 50-row theater is 5900.

1. Consider the following 2 sets of data that list football teams and
quarterbacks:
D = {Jets, Giants, Cowboys, 49’ers, Patriots, Rams, Chiefs}
Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli
Manning}

2. I like making NFL Matrices before placing it
into a function / relation graph. This way I
have all information in on table verses being
all over the place.

3. TEAMS PLAYERS
JETS JOE NAMATH
RAMS
CHEIFS
49’ers JOE MONTANA
GIANTS ELI MANNING
PATRIOTS TOM BRADY
COWBOYS TROY AIKEN
In this slide the matrix is turned into:
Set of ordered pairs
Directional graph
The sets will result in the ordered pairs of : ( Jets, Joe
Namath) (Rams, Joe Namath) (Chiefs, Joe Montana)
(49’ers, Joe Montana) ( Giants, Eli Manning) (Patriots,
Tom Brady) and (Cowboys, Troy Aiken). It IS a
function as it does have a one-to-one functional output
within the range area. Certain inputs have relative
outputs of more than one. This does NOT. Therefore,
it’s a FUNCTION!!!

4. TEAMS PLAYERS
JETS
JOE NAMATH RAMS
TROY AIKEN COWBOYS
JOE MONTANA CHEIFS
49’ers
TOM BRADY PATRIOTS
ELI MANNING GIANTS
In this slide the matrix is turned into:
Set of ordered pairs
Directional graph
The sets will result in the ordered pairs of : (Joe
Namath, Jets) (Joe Namath, Rams) (Joe Namath, Jets,
Rams) (Joe Montana, 49’ers) (Joe Montana, Chiefs)
(Joe Montana, 49’ers, Chiefs) (Giants, Eli Manning)
(Patriots, Tom Brady) and (Cowboys, Troy Aiken). It is
“NOT” a function as it does “NOT” have a one-to-one
functional output within the range area. Certain inputs
have relation outputs of more than one. Therefore, it’s
a RELATION!!

5. PART II
• Mathematical sequences can be used to model real life
applications. Suppose you want to construct a movie theater
in your town. The number of seats in each row can be
modeled by the formula Cn = 16 + 4n, when n refers to the
nth row, and you need 50 rows of seats.
• (a) Write the sequence for the number of seats for the first
5 rows
• (b) How many seats will be in the last row?
• (c) What will be the total number of seats in the theater?

6. • The formula Cn = 16 + 4n should be written in the explicit formula dimension. The
first five rows of seats would be drawn out in the following mathematical order.
This would continue up to the Cn = 50, which is row 50.
• C = {C(n)} = {Cn} = n ϵ N . (N) is the index of the sequence.
• C = {C1, C2, C2, ... Cn, …}. In this case to the C50 row.
C1 = 16 + 4(1) = 20 C14 = 16 + 4(14) = 72 C27 = 16 + 4(27) = 124 C40 = 16 + 4(40) = 176
C2 = 16 + 4(2) = 24 C15 = 16 + 4(15) = 76 C28 = 16 + 4(27) = 128 C41 = 16 + 4(41) = 180
C3 = 16 + 4(3) = 28 C16 = 16 + 4(16) = 80 C29 = 16 + 4(29) = 132 C42 = 16 + 4(42) = 184
C4 = 16 + 4(4) = 32 C17 = 16 + 4(17) = 84 C30 = 16 + 4(30) = 136 C43 = 16 + 4(43) = 188
C5 = 16 + 4(5) = 36 C18 = 16 + 4(18) = 88 C31 = 16 + 4(31) = 140 C44 = 16 + 4(44) = 192
C6 = 16 + 4(6) = 40 C19 = 16 + 4(19) = 92 C32 = 16 + 4(32) = 144 C45 = 16 + 4(45) = 196
C7 = 16 + 4(7) = 44 C20 = 16 + 4(20) = 96 C33 = 16 + 4(33) = 148 C46 = 16 + 4(46) = 200
C8 = 16 + 4(8) = 48 C21 = 16 + 4(21) = 100 C34 = 16 + 4(34) = 152 C47 = 16 + 4(47) = 204
C9 = 16 + 4(9) = 52 C22 = 16 + 4(22) = 104 C35 = 16 + 4(35) = 156 C48 = 16 + 4(48) = 208
C10 = 16 + 4(10) = 56 C23 = 16 + 4(23) = 108 C36 = 16 + 4(36) = 160 C49 = 16 + 4(49) = 212
C11 = 16 + 4(11) = 60 C24 = 16 + 4(24) = 112 C37 = 16 + 4(37) = 164 C50 = 16 + 4(50) = 216
C12 = 16 + 4(12) = 64 C25 = 16 + 4(25) = 116 C38 = 16 + 4(38) = 168
C13 = 16 + 4(13) = 68 C26 = 16 + 4(26) = 120 C39 = 16 + 4(39) = 172

7. 1. The sequence for the first five rows would be as follows:
• C1 = 16 + 4(1) = 20
• C2 = 16 + 4(2) = 24
• C3 = 16 + 4(3) = 28
• C4 = 16 + 4(4) = 32
• C5 = 16 + 4(5) = 36
• The first five rows would be related to the sum of the series if only using
the first five rows as the example area.
• The equation would correlate to
• Σ cn = c1 + c2 + … + cn
•Σ (16 + 4n) = 20 + 24 +28 + 32 + 36 = 140
• The sum of the terms of a Sequence is called a Series as established
above.
n
n = 1
n = 1
5

8. Once calculation of all 50 rows is accomplished we can see
that the last row (50th row) will have 216 seats. All combined
there will be 5900 seats in the theater.
C1 = 16 + 4(1) = 20 C14 = 16 + 4(14) = 72 C27 = 16 + 4(27) = 124 C40 = 16 + 4(40) = 176
C2 = 16 + 4(2) = 24 C15 = 16 + 4(15) = 76 C28 = 16 + 4(27) = 128 C41 = 16 + 4(41) = 180
C3 = 16 + 4(3) = 28 C16 = 16 + 4(16) = 80 C29 = 16 + 4(29) = 132 C42 = 16 + 4(42) = 184
C4 = 16 + 4(4) = 32 C17 = 16 + 4(17) = 84 C30 = 16 + 4(30) = 136 C43 = 16 + 4(43) = 188
C5 = 16 + 4(5) = 36 C18 = 16 + 4(18) = 88 C31 = 16 + 4(31) = 140 C44 = 16 + 4(44) = 192
C6 = 16 + 4(6) = 40 C19 = 16 + 4(19) = 92 C32 = 16 + 4(32) = 144 C45 = 16 + 4(45) = 196
C7 = 16 + 4(7) = 44 C20 = 16 + 4(20) = 96 C33 = 16 + 4(33) = 148 C46 = 16 + 4(46) = 200
C8 = 16 + 4(8) = 48 C21 = 16 + 4(21) = 100 C34 = 16 + 4(34) = 152 C47 = 16 + 4(47) = 204
C9 = 16 + 4(9) = 52 C22 = 16 + 4(22) = 104 C35 = 16 + 4(35) = 156 C48 = 16 + 4(48) = 208
C10 = 16 + 4(10) = 56 C23 = 16 + 4(23) = 108 C36 = 16 + 4(36) = 160 C49 = 16 + 4(49) = 212
C11 = 16 + 4(11) = 60 C24 = 16 + 4(24) = 112 C37 = 16 + 4(37) = 164 C50 = 16 + 4(50) = 216
C12 = 16 + 4(12) = 64 C25 = 16 + 4(25) = 116 C38 = 16 + 4(38) = 168
C13 = 16 + 4(13) = 68 C26 = 16 + 4(26) = 120 C39 = 16 + 4(39) = 172

9. Again, by using the sequence formula for addition to find the sum, the
equation will look something of the following:
Σ (16 + 4n) =
20 + 24 +28 + 32 + 36 + 40 + 44 + 48 + 52 + 56 + 60 + 64 + 68 + 72 + 76 +
80 + 84 + 88 + 92 + 96 + 100 + 104 + 108 + 112 + 116 + 120 + 124 + 128 +
132 + 136 + 140 + 144 + 148 + 152 + 156 + 160 + 164 +168 + 172 + 176 +
180 + 184 + 188 + 192 + 196 + 200 + 204 + 208 + 212 + 216 = 5900 seats.
50
n = 1