Download 1. Which expression can be used to find the nth term in the following

Objective 2: Patterns, Relationships, & Algebraic Reasoning
8.5B: The student uses graphs, tables, and algebraic representations to make predictions
and solve problems. The student is expected to find and evaluate an algebraic expression
to determine any term in an arithmetic sequence (with a constant rate of change).
(Supporting)
1. Which expression can be used to find the nth term in the following arithmetic sequence,
where n represents a number’s position in the sequence?
A
B
C
D
Position in
Sequence
1
2
3
4
n
Term
5
9
13
17
?
n+4
3n + 4
5n
4n + 1
2. Let n represent the position of a number in the following arithmetic sequence.
1
3
, 1,
, 2, …
2
2
Which expression can be used to find any term in the sequence?
F
2n
G
1
n
2
H
3
n
2
J
5
n
2
1
Objective 2: Patterns, Relationships, & Algebraic Reasoning
3. In the sequence below, which expression can be used to find the value of the term in the
nth position?
Position
Value of Term
1
0.25
2
0.5
3
0.75
4
1.0
5
1.25
n
F
n − 0.75
G
n
4
H
4n
J
n − 1.5
4. The expression shown below describes a pattern of numbers.
n(n − 1) + 4
If n represents a number’s position in the sequence, which pattern of numbers does the
expression describe?
A
B
C
D
4, 6, 8, 10, 12, . . .
1, 4, 6, 10, 16, . . .
4, 6, 10, 16, 24, . . .
4, 10, 18, 28, 40, . . .
2
Objective 2: Patterns, Relationships, & Algebraic Reasoning
5.
Which expression can be used to
find the nth term, where n represents
the position of the term in the
sequence?
Position
6.
Which expression can be used to
find the nth term, where n
represents the position of the term
in the sequence?
Position
1
2
3
5
n
Value of
Term
1
2
3
6
n
-2
-2
0
18
A
Value of Term
1
1.5
2
3
?
n 1
2
A n2
B n+
B 3n
7.
1
2
C n2  3n
C n2
D n2  3
D n2 – 2.5
Let n represent the position of a
number in the following sequence
-2, 1, 4, 7, …
8.
If n is the position of a number in
this sequence, which expression
would help you find the value of the
nth term?
Position
1
2
5
7
n
Which expression can be used to
find any term in the sequence?
A 3n – 5
B n+3
Value
0
2
20
42
?
C 2n – 1
A n–1
D -2n
B n(n – 1)
C 2n – 2
D n
3
Objective 2: Patterns, Relationships, & Algebraic Reasoning
9.
Let n represent the position of a
number in the following sequence
-1, 1, 3, 5, …
Which expression can be used to
find any term in the sequence?
A –1n
B 2n – 3
C n+2
D 3n – 4
10.
If n represents the figure number, which expression can be used to find the number of tiles in
any figure?
Figure 1
Figure 2
Figure 3
Figure 4
A n+3
B 3n
C n(n + 1)
D n+2
4
Objective 2: Patterns, Relationships, & Algebraic Reasoning
11.
Figure 1
Figure 2
Figure 3
Figure 4
If n represents the figure number, which expression can be used to find the number of tiles in any figure?
12.
A
2n
B
2(n + 1)
C
n+1
D
2n + 1
If n represents the figure number in the sequence shown below, which expression can be used to find the number
of dots in any figure?
A
n
B
n+2
C
2n + 1
D
2n - 1
Figure 1
Figure 2
Figure 3
Figure 4
5
Objective 2: Patterns, Relationships, & Algebraic Reasoning
13.
Figure 1
Figure 2
Figure 3
Based on this pattern how many tiles will be used to draw Figure 11?
Figure 4
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
6
Objective 2: Patterns, Relationships, & Algebraic Reasoning
14.
The Sandbox Design Company builds sandboxes with wooden tiles placed around the outside of
the sand for children to sit on as shown in the diagrams below.
Sandbox
1
Sandbox
2
Sandbox
3
= wooden tile
Sandbox
4
= sand
If n represents the sandbox number, which expression can be used to find the number of wooden
tiles in any figure?
15.
A
n+7
B
4n + 4
C
4n
D
(n + 2)2
Matilda looked at a set of data and made the conjecture that the y-value is twice the x-value increased by one.
Which set of data does NOT match Matilda’s conjecture?
A
x
y
1
3
2
5
3
7
4
9
5
11
B
x
y
-4
-7
-2
-3
0
1
2
5
4
8
C
x
y
3
7
5
11
7
15
9
19
11
23
D
x
y
-3
7
-2
5
-1
3
0
1
1
3
7
Objective 2: Patterns, Relationships, & Algebraic Reasoning
16.
In the sequence below, which sequence
CANNOT be used to find the value of the
term in the nth position?
Position
1
2
3
4
5
n
A
2x  2
B
2( x  3)
C
2( x  4)  2
D
2x  2  8
Value of Term
8
10
12
14
16
8