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Name: _______________________________
Block: ___________ Date: ______________
Patterns and Sequences
Sequence: a list of numbers in a
.
Arithmetic Sequence: a sequence created by
the
same number to or from each term in the list.
Geometric Sequence: a sequence created by
each term
in the list by the same number.
Common difference: the constant number that is _________________to each term to find the
next term in a _____________________ sequence.
Common ratio: the constant number that is _________________ to each term to find the next
term in a _________________ sequence.
How do I find the pattern?
Step 1: Study the numbers that are shown
Step 2: Ask, “How do you get to the next number in the pattern?” (common difference or ratio)
Step 3: Find the next number(s)
Step 4: Write the sequence as an expression
Let’s try some together!
1)
1
2
14, 16 , 19, _______, ________
2) -4 , 8 , -16 , 32, __________, __________
Common Ratio/Difference:_______________
Type of Sequence:______________________ Common Ratio/Difference:______________
Expression:___________________________ Type of Sequence:_____________________
Expression:___________________________
3) 10 , 5 , 0 , -5, __________ , __________
4) 100 , 10 , 1 , 0.1 , ________ , _________
Common Ratio/Difference:_______________ Common Ratio/Difference:______________
Type of Sequence:______________________ Type of Sequence:_____________________
Expression:____________________________ Expression:___________________________
Now you try!
1)
1
, 2 , 8 , 32 , ________, ________
2
2) 1 , 2, 4 , 7 , __________, __________
Common Ratio/Difference:_______________ Common Ratio/Difference:______________
Type of Sequence:______________________ Type of Sequence:_____________________
Expression:____________________________ Expression:___________________________
3) 18 , 15 , 12 , 9 , _________, __________
4) 0.4 , 0.8 , 1.2 , 1.6 , _________, ________
Common Ratio/Difference:_______________ Common Ratio/Difference:______________
Type of Sequence:______________________ Type of Sequence:_____________________
Expression:____________________________ Expression:___________________________
Find the missing number:
1) 4 , _________, 36 , 108
3) _________, 32 , 20 , 8
2) 5 , 20 , _________, 50
4) 1 , 3.3 , 5.6 , _________
Find the seventh term in the sequence:
1) 3 , 6 , 12 , 24…
_________________
Patterns and Sequences Practice
1) Which sequence follows the variable expression 𝑛𝑛 − 13
2) Which sequence follows the variable expression
𝑥𝑥
3
3) Which sequence follows the variable expression x - 99
4) Robin is going to create a sequence with a common difference of -17. She wants to ensure
that the number 22 is included in her sequence. Which number could she choose to begin
her sequence with?
104
105
106
5) What is the 6th term of the geometric sequence?
107
80, 40, 20, …
6) Ginni wrote the following geometric sequence in her notebook: 3, 9, 27, 81, 243, 729…
What would be the 8th term in Ginni’s sequence?
7) Which sequence used the variable expression y + 1.4 to define the next term?
Sequence 1
-3.17, -4.57, -5.97, -7.37, -8.77, …
Sequence 2
5.73, 7.13, 8.53, 9.93, 11.33, …
Sequence 3
2, 2.8, 3.92, 5.488, 7.6832, …
Sequence 4
-1, -1.4, -1.96, -2.744, -3.8416, …
Patterns and Sequences Homework
1. Which of the following is/are geometric
sequence(s)?
a. 2, 4, 8, 16….
b. 1, -10, 100, -1000….
c. 19, 17, 16, 10…..
d. -10, -8, -6, -4…..
2. Which of the following is an arithmetic
sequence?
a. 3, 9, 27, 81…
b. -2, -1, -1/2, -1/4….
c. 110, 210, 310, 410…
d. 1, 4, 40, 100…..
3. A(n) ___________ sequence has a
common difference.
4. A(n) __________ sequence has a common
ratio.
5. What variable expression describes the
relationship between consecutive terms
in this sequence? 3, 9, 27, 81…
6. Emily made an arithmetic sequence with
consecutive terms related by this rule:
n + (-5)
Which of these is Emily’s sequence?
a. 15, 20, 25, 30…
b. 60, 55, 50, 45…
c. 5, 55, 555, 5555….
7. Michelle wrote this variable expression
to describe the relationship between
consecutive terms in her sequence:
0.5n
Which is Michelle’s sequence?
a. 10, 50, 250, 1250….
b. 0.5, 1.5, 2.5, 3.5…
c. 36, 18, 9, 4.5….
d. 3, 6, 12, 24…..
8. Fill in the missing term in this geometric
sequence:
9. What will be the next term in this
arithmetic sequence:
10.Fill in the terms in this sequence that starts
with 2 and has a common ratio of -5:
-5.5, -4, -2.5, -1, _______
32, 8, ____, 0.5
2, ______, ______, _______, _____, ______
11) Complete the table with an expression that describes each sequence.
SEQUENCE
EXPRESSION
p+5
-1, -3, -9, -27 …
15, 20, 25, 30…
4r
-6, -4, -2, 0 …
3t
¼ , 1, 4, 16 …
b+2
12) Which sequence has a common ratio of 3?
13) Which sequence has a common difference of -13?
14) Look at the following sequence.
50, 10, 2,
2
5
15) Ginni wrote the following geometric
sequence in her notebook
…
3, 9, 27, 81, 243, 729, …
What variable expression describes the
relationship between the terms in the
sequence?
What would be the 8th term in Ginni’s
sequence?
16) What is the common difference of the arithmetic sequence shown below?
-4, -8, -12, -16 …
a) 4
b) 2
c) -2
d) -4