MATH 8 PATTERNS & SEQUENCES

MATH 8
1.
PATTERNS & SEQUENCES
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?
Position in
Sequence
Term
A. n + 4
2.
3.
NAME___________________________
1
2
3
4
n
5
9
13
17
?
B. 3n + 4
C. 5n
D. 4n + 1
What expression can be used to find the nth term in this sequence? 4, 8, 12, 16, ...
Hint: Look at the relationship between the terms in the sequence and their position in the sequence.
Position in
Sequence
1
2
3
4
...
Value of Term
4
8
12
16
...
n
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
4.
G.
1
n
2
3
H. n
2
J.
5
n
2
What expression could be used to find the nth term?
4, 7, 10, 13, . . .
Position
Value of Term
1
4
5.
What is the 15th term in this sequence?
6.
Look at this sequence of numbers.
2
7
3
10
4
13
...
...
n
–4, –6, –8, –10, –12, . . .
Does the expression –2(n + 1) show the relationship between any term and n, its position in the
sequence? ________________
7.
A sequence of numbers was formed using the rule 2n – 3, where n represents the number’s position
in a sequence. Which sequence fits this rule?
A. 0, 1, 3, 4, 6, …
B. 1, 2, 3, 4, 5, …
C. 2, 4, 6, 8, 10, …
D. –1, 1, 3, 5, 7, …
8.
Let n represent a term’s position in a sequence. Which algebraic expression can be used to
find the nth term of this sequence?
4, 12, 24, 40, 60, …
A. 2n(n + 1)
9.
F. n  0.75
11.
2
3
4
5
n
0.25
0.5
0.75
1.0
1.25
?
G.
A.
2 3 4 5 6
, , ,
,
, ...
3 6 9 12 18
B.
1 3 4 5 6
, , ,
,
, ...
3 6 9 12 15
n
4
J. n 15
.
H. 4n
C. 0,
D.
2 3 4 5
, , ,
, ...
3 6 9 12
2 3 4 5 6
, , ,
,
, ...
3 6 9 12 15
This expression 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?
B. 1, 4, 6, 10, 16,…
C. 4, 6, 10, 16, 24, ... D. 4, 10, 18, 28, 40, ...
This expression describes a pattern of numbers.
2n + 3
If n represents a number’s position in the sequence, which pattern of numbers does the expression
describe?
B. 3, 5, 8, 13, 21, …
C. 5, 7, 10, 14, 19, ...
D. 5, 7, 9, 11, 13, ...
This expression describes a pattern of numbers.
2n2  1
If n represents a number’s position in the sequence, which pattern of numbers does the expression
describe?
A. 20, 21, 22, 23, 24, ...
14.
1
n 1
, where n represents the number’s
3n
position in a sequence. Which sequence fits this rule?
A. 24, 25, 26, 27, 28, ...
13.
D. n² + 3
A sequence of numbers was formed using the rule
A. 4, 6, 8, 10, 12, ...
12.
C. 4n²
In the sequence below, which expression can be used to find the value of the term in the nth position?
Position in
Sequence
Term
10.
B. 4n
B. 1, 7, 17, 31, 49, …
C. 1, 5, 9, 13, 17, ...
D. 1, 7, 17, 27, 37, ...
A sequence of numbers was formed using the rule n(2n + 1) – 2, where n represents a number’s
position in the sequence. Which pattern of numbers does the expression describe?
A. 1, 3, 5, 7, 9,…
B. 1, 8, 19, 34, 53, ...
C. 1, 4, 8, 12, 16, ...
D. 1, 7, 17, 31, 50, ...
15. Let n represent the term’s position in the following sequence.
Write an expression to represent this sequence.
16. Write an expression to represent the
pattern in the table.
17. Write an algebraic expression to describe the pattern.
18. Write an algebraic expression to describe the pattern.
5, 13, 21, 29, 37 …….