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Objective
Recognize and extend patterns for
sequences
Vocabulary
Sequence
An ordered list of numbers
Vocabulary
Term
Each number in a sequence
8, 11, 14, 17, 20 . . .
Vocabulary
Arithmetic sequence
Each term is found by adding the same
number to the previous term
8, 11, 14, 17, 20 . . .
3 is added to each term to get the next term
Vocabulary
Geometric sequence
Each term is found by multiplying the
previous term by the same number
3, 6, 12, 24, 48 . . .
2 is multiplied to each term to get the next
term
Example 1 Describe Patterns in Sequences
Example 2 Describe Patterns in Sequences
Example 3 Determine Terms in Sequences
Example 4 Determine Terms in Sequences
Describe the pattern in the sequence and identify the
sequence as arithmetic, geometric, or neither.
3, 6, 12, 24, …
3, 6, 12, 24, …
Write problem
Determine how the series goes
from the 3 to the 6
Remember: Sometimes there
is more than one way
Add 3
or
Multiply by 2
Which pattern will get the 6 to 12?
1/4
Describe the pattern in the sequence and identify the
sequence as arithmetic, geometric, or neither.
3, 6, 12, 24, …
3, 6, 12, 24, …
  
Add 3
or
Multiply by 2
Which pattern will get the 6 to 12?
Does multiplying by 2 get the 12
to the 24?
The pattern is multiplying by 2
The pattern is multiplying by 2
1/4
Describe the pattern in the sequence and identify the
sequence as arithmetic, geometric, or neither.
3, 6, 12, 24, …
3, 6, 12, 24, …
  
Geometric
Add 3
or
Multiply by 2
Name the sequence
Remember:
Arithmetic is adding the same number
Geometric is multiplying the same number
Multiply by 2
Answer: Multiplying by 2 ; geometric
1/4
Describe the pattern in the sequence and identify the
sequence as arithmetic, geometric, or neither.
5, 9, 18, 22, 31, …
Answer: Add 4, add 9; neither.
1/4
Describe the pattern in the sequence and identify the
sequence as arithmetic, geometric, or neither.
7, 11, 15, 19, …
Write problem
7, 11, 15, 19, …
Determine how the series goes
from the 7 to the 11
Remember: Sometimes there
is more than one way
Add 4
Determine how the series goes
from the 11 to the 15
Add 4
2/4
Describe the pattern in the sequence and identify the
sequence as arithmetic, geometric, or neither.
7, 11, 15, 19, …
Determine how the series goes
from the 15 to the 19
7, 11, 15, 19, …
Add 4
The pattern is adding 4
Arithmetic
Now identify the pattern
Pattern is adding the same
number each time
Answer: Add 4; Arithmetic sequence
2/4
Describe the pattern in the sequence and identify the
sequence as arithmetic, geometric, or neither.
3, 11, 19, 27, …
Answer: Add 8; arithmetic.
2/4
Write the next three terms of the sequence.
5, 14, 23, 32, ...
Write problem
5, 14, 23, 32, …
Determine how the series goes
from the 5 to 14
Remember: Sometimes there
is more than one way
Add 9
Determine how the series goes
from the 14 to 23
Add 9
3/4
Write the next three terms of the sequence.
5, 14, 23, 32, ...
Determine how the series goes
5, 14, 23, 32, …
from the 23 to 32
Add 9
Use the pattern of adding 9 to
determine the next three terms
Add 9 to 32
Add 9 to 41
Add 9 to 50
Answer: 41, 50, and 59.
3/4
Write the next three terms of the sequence.
12, 17, 22, 27, …
Answer:
32, 37, 42
3/4
Write the next three terms of the sequence.
0.2, 1.2, 7.2, 43.2, …
Write problem
0.2, 1.2, 7.2, 43.2,
6
6
Determine how the series goes
from the 0.2 to 1.2
Remember: Sometimes there
is more than one way
Add 1
and multiply 6
Determine how the series goes
from the 1.2 to 7.2
Adding 1 does not work
Multiply by 6 does work
4/4
Write the next three terms of the sequence.
0.2, 1.2, 7.2, 43.2, …
Determine how the series goes
from the 7.2 to 43.2
0.2, 1.2, 7.2, 43.2,
Multiply by 6
6
6
6
9,331.2
Answer:
Use the pattern of multiplying
by 6 to determine the next three
terms
Multiply 43.2 by 6
Multiply 259.2 by 6
Multiply 1,555.2 by 6
259.2, 1,555.2, and 9,331.2
4/4
*
Write the next three terms of the sequence.
3, 12, 48, 192, …
Answer:
768, 3,072, 12,288
4/4
Assignment
Lesson 1:7
Sequences
4 - 24 All