Download Sequences

Math 6 NOTES (6.4)
Name ____________________________________
Sequences
A sequence is an ordered list of numbers, with terms that follow a mathematical rule.
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•
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Each number in a sequence is called a ________________________.
The rule of the sequence describes the _______________________.
In an Arithmetic Sequence, the difference between any two consecutive terms is the
same. So, you can find the next term in the sequence by adding the same number (positive or
negative) to the previous term.
8 , 11 , 14 , 17 , 20 , 23
+3
+3
+3
+3
+3
29 , 23 , 17 , 11 , 5 , -1
+(-6) +(-6) +(-6) +(-6) +(-6)
o The difference between any two consecutive terms in arithmetic sequence is called the
____________________________________.
Continue the patterns below with the next three terms. What rule does each pattern follow?
1) 5, 10, 15, _____ , _____ , _____
2) 2, 4, 6, 8, _____ , _____ , _____
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3) 100, 75, 50, _____ , _____ , _____
Rule:____________________________________________________
Rule:____________________________________________________
Rule:____________________________________________________
In a Geometric Sequence, the quotient of any two consecutive terms is the same. So, you
can find the next term in the sequence by multiplying the previous term by the same number
(whole or fraction) to the previous term.
3 , 6 , 12 , 24 , 48
·2
·2
·2
·2
4 , 2 , 1 ,
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o The factor between any two consecutive terms in geometric sequence is called the
____________________________________.
Continue the patterns below with the next three terms. What rule does each pattern follow?
4) 2 , 4 , 8 , 16 , _____ , _____ , _____
Rule:____________________________________________________
6) 1 , 4 , 16 , _____ , _____ , _____
Rule:____________________________________________________
5)
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, , 1 , 2 , _____ , _____ , _____
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Rule:____________________________________________________
A sequence that does not have a common difference or common ratio is NEITHER an
arithmetic or geometric sequence.
1, 2, 4, 7, 11
+1 +2 +3 +4
Math 6 PRACTICE (6.4)
Name ____________________________________
Identify the pattern as an arithmetic sequence, a geometric sequence, or neither. Then describe
the relationship (rule) between two consecutive terms.
1.)
3.)
5)
7)
9)
2, 3, 4, 5, 6, …
________________________________
________________________________
2)
35, 28, 21, 14, …
________________________________
________________________________
6)
8, 13, 18, 23, 28, …
________________________________
________________________________
4)
2, 4, 8, 16, …
________________________________
________________________________
8)
8, 6, 4, 2
________________________________
________________________________
10)
1, 2, 4, 8, 16, …
_________________________________
_________________________________
5, 6, 8, 11, 15, …
_________________________________
_________________________________
1, 3, 9, 27, …
_________________________________
_________________________________
121, 1221, 12221, …
_________________________________
_________________________________
2, 6, 24, 120
_________________________________
_________________________________
11) What is the common ratio of the geometric sequence shown?:
8, 32, 128, …
13) Find the missing terms in the sequence:
26, 33, 40, ____, 54, 61, ____, …
12) What is the 7th term of the arithmetic sequence?:
Write the next three terms of the following sequences.
29, 21, 13, 5, …
14) 0, 13, 26, 39, _____, _____, _____
15) 8, 5, 2, -1, -4, _____, _____, _____
16) 2, 6, 18, 54, _____, _____, _____
17) Create three patterns. Then describe the relationship (rule) between each consecutive term.
Arithmetic: ____________________________________________________ Rule: _________________________________
Geometric: ____________________________________________________ Rule: __________________________________
Neither:
____________________________________________________ Pattern: _______________________________
Find the pattern in each sequence and identify the sequence as Arithmetic, Geometric, or Neither.
1, 6, 36, 216, ...
What is the pattern? _________
What type of sequence is this? ______________________
2, 5, 8, 11, …
What is the pattern? _________
What type of sequence is this? ______________________
3, 6, 10, 15, …
What is the pattern? _________
What type of sequence is this? ______________________
Identify the next three terms in each sequence. Is the sequence as Arithmetic, Geometric, or
Neither?
1). 3, 6, 9, 12, _____, ______, ______
2). 20, 30, 40, 50, ______, ______, ______
Type of Sequence: _______________
Type of Sequence: ___________________
3). 1, 2, 4, 8, ______, ______, ______
4). 2, 6, 18, ______, ______, ______
Type of Sequence: _______________
Type of Sequence: ___________________
5). 14, 16, 18, ______, ______, ______
6). 3, 9, 27, ______, ______, ______
Type of Sequence: ________________
Type of Sequence: ___________________
7). 5, 7, 9, 11, ______, ______, ______
8.) 1, 5, 25, ______, ______, ______
Type of Sequence: ________________
Type of Sequence: ____________________
9.) 9, 16, 23, 30, ______, ______, ______
10.) 5, 15, 45, 135, ______, ______, ______
Type of Sequence: ________________
Type of Sequence: ____________________
11.) 12, 48, 192, 768, ______, ______, _____
12.) 4, 12, 20, 28, _____, _____, _____
Type of Sequence: ________________
Type of Sequence: ____________________