12-2
Find a Pattern in Sequences
Learn to find patterns to complete
sequences using function tables.
Course 2
12-2
Insert
Lesson Title
Here
Find
a Pattern
in Sequences
Vocabulary
sequence
Course 2
12-2
Find a Pattern in Sequences
A sequence is an ordered list of numbers. One
of the most well-known sequences is the
Fibonacci sequence. In this sequence, each term
after the second term is the sum of the two
terms before it.
1, 1, 2, 3, 5, 8, 13,…
When the list follows a pattern, the numbers in
the sequence are the output values of a function,
and the value of each number depends on the
number’s place in the list is the input.
Course 2
12-2
Find a Pattern in Sequences
You can use a variable to represent a number’s
place in a sequence.
n
(place in list)
INPUT
1st number 2nd number 3rd number 4th number
Number
in sequence:
OUTPUT
You can use a function table to help identify the
pattern in a sequence.
Course 2
12-2
Find a Pattern in Sequences
Additional Example 1A: Identifying Functions in a
Sequence
Find a function that describes each sequence. Use y for
the term in the sequence and n for its place in the list.
Then use the function to find the next three terms in
the sequence.
A. 4, 8, 12, 16, . . .
Course 2
x
Rule
y
1
1·4
4
2
2·4
8
3
3·4
12
4
4·4
16
Multiply n by 4.
12-2
Find a Pattern in Sequences
Additional Example 1A Continued
Use the function to find the next three terms
in the sequence.
A. 4, 8, 12, 16, . . .
y = 4x
Write the function.
y = 4(5) = 20
Substitute for n to find
the next three terms.
y = 4(6) = 24
y = 4(7) = 28
Course 2
12-2
Find a Pattern in Sequences
Additional Example 1B: Identifying Functions in
Sequences
Find a function that describes the sequence. Use y for
the term in the sequence and n for its place in the list.
Then use the function to find the next three terms in
the sequence.
B. –4, –3, –2, –1, . . .
Course 2
x
Rule
y
1
1–5
–4
2
2–5
–3
3
3–5
–2
4
4–5
–1
Subtract 5 from n.
12-2
Find a Pattern in Sequences
Additional Example 1B Continued
Use the function to find the next three
numbers in the sequence.
B. –4, –3, –2, –1, . . .
y=x–5
Write the function.
y = (5) – 5 = 0
Substitute for n to find
the next three terms.
y = (6) – 5 = 1
y = (7) – 5 = 2
Course 2
12-2
Insert
Here
Find a Lesson
Pattern Title
in Sequences
Try This: Example 1
Find a function that describes each sequence. Use y for
the term in the sequence and n for its place in the list.
Then use the function to find the next three terms in
the sequence.
A. 3, 6, 9, 12, . . .
x
Rule
y
1
1·3
3
2
2·3
6
3
3·3
4·3
9
4
Course 2
12
Multiply n by 3.
12-2
Insert
Here
Find a Lesson
Pattern Title
in Sequences
Try This: Example 1A Continued
Use the function to find the next three terms
in the sequence.
A. 3, 6, 9, 12, . . .
y = 3x
Write the function.
y = 3 (5) = 15
Substitute for n to find
the next three numbers
y = 3 (6) = 18
y = 3 (7) = 21
Course 2
12-2
Insert
Here
Find a Lesson
Pattern Title
in Sequences
Try This: Example 2
Bob spends $12.50 each week for a lunch
ticket. In addition, he usually spends
$6.50 a day for incidentals. Write a
sequence showing how much money Bob
had spent after 1, 2, 3, 4, and 5 days.
Course 2
Insert
Here
Find a Lesson
Pattern Title
in Sequences
12-2
3
Try This: Example 2 Continued
Solve
n
Rule
y
1
1 · 6.50 + 12.5
19.00
2
2 · 6.50 + 12.5
25.50
3
3 · 6.50 + 12.5
32.00
4
4 · 6.50 + 12.5
38.50
5
5 · 6.50 + 12.5
45.00
After 1, 2, 3, 4 and 5 days, Bob will have
spent $19.00, $25.50, $32.00, $38.50,
and $45.00, respectively.
Course 2
12-2
Find
Insert
a Pattern
Lesson Title
in Sequences
Here
Lesson Quiz: Part 1
Find a function that describes each sequence.
Use the function to find the next three terms in
the sequence.
1. 6, 12, 18, 24
y = 6n; 30, 36, 42
2. –3, –2, –1, 0
y = n – 4; 1, 2, 3
3. 24, 21, 18, 15
y = 27 – 3n; 12, 9, 6
4. 7, 14, 21, 28
y = 7n; 35, 42, 49
Course 2