1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Find the output for each input value.
Warm Up
Find the output for each input value.
Input
Rule
Output x
–3x + 2 y –4 14 2 4
–10

3. Function Rule A: Square the input. Divide by 2. Subtract 3.
Problem of the Day
Function Rule A: Square the input. Divide by 2. Subtract 3.
Function Rule B: Square the input. Subtract 6. Divide by 2.
If the input value for each rule is 222, what is the difference of the two output values? Why?
0; they are equivalent rules.

4. Learn to find patterns to complete sequences using function tables.

5. Vocabulary sequence term arithmetic sequence common difference
geometric sequence

6. A sequence is an ordered list of numbers
A sequence is an ordered list of numbers. Each number in a sequence is called a term.
When the sequence follows a pattern, the terms 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.

7. n (position in the sequence)‏
You can use a variable such as n, to represent a number’s position in a sequence. 8 6 4 2
y (value of term)‏ 3 1
n (position in the sequence)‏
In an arithmetic sequence, the terms of the sequence differ by by the same nonzero number. This difference is called the common difference. In a geometric sequence, each term is multiplied by the same amount to get the next term in the sequence.

8. Additional Example 1A: Identifying Patterns in a Sequence
Tell whether the sequence of y-values is arithmetic or geometric. Then find y when n = 5.
-64
-16 -4 -1 y 5 4 3 2 1 n
-256
In the sequence -1, -4, -16, -64, ,…, each number is multiplied by 4.
-64 ● 4 = -256.
Multiply the fourth number by 4.
The sequence is geometric. When n = 5, y = -256.

9. Additional Example 1B: Identifying Patterns in a Sequence
Tell whether the sequence of y-values is arithmetic or geometric. Then find y when n = 5. 36 41 46 51 y 5 4 3 2 1 n 31
In the sequence 51, 46, 41, 36, ,…, -5 is added each time.
36 + (-5) = 31.
Add -5 to the fourth number.
The sequence is arithmetic. When n = 5, y = 31.

10. Check It Out: Example 1A
Tell whether the sequence of y-values is arithmetic or geometric. Then find y when n = 5. 24 20 16 12 y 5 4 3 2 1 n 28
In the sequence 12, 16, 20, 24, ,…, 4 is added each time.
= 28.
Add 4 to the fourth number.
The sequence is arithmetic. When n = 5, y = 28.

11. -27 -9 -3 -1 y 5 4 3 2 1 n Check It Out: Example 1B
Tell whether the sequence of y-values is arithmetic or geometric. Then find y when n = 5.
-27 -9 -3 -1 y 5 4 3 2 1 n
-81
In the sequence -1, -3, -9, -27, ,…, each number is multiplied by 3.
-27 ● 3 = -81.
Multiply the fourth number by 3.
The sequence is geometric. When n = 5, y = -81.

12. Additional Example 2A: Identifying Functions in Sequences
Write a function that describes the sequence.
3, 6, 9, 12,…
Make a function table. 12 4 9 3 6 2 1 y
Rule n
1 • 3
2 • 3
Multiply n by 3.
3 • 3
4 • 3
The function y = 3n describes this sequence.

13. Additional Example 2B: Identifying Functions in Sequences
Write a function that describes the sequence.
4, 7, 10, 13,…
Make a function table. 13 4 10 3 7 2 1 y
Rule n
3(1) + 1
3(2) + 1
Multiply n by 3 and add 1.
3(3) + 1
3(4) + 1
The function y = 3n + 1describes this sequence.

14. Check It Out: Example 2A
Write a function that describes the sequence.
5, 6, 7, 8,…
Make a function table. 8 4 7 3 6 2 5 1 y
Rule n
1 + 4
2 + 4
Add 4 to n.
3 + 4
4 + 4
The function y = 4 + n describes this sequence.

15. Check It Out: Example 2B
Write a function that describes the sequence.
3, 4, 5, 6,…
Make a function table. 6 10 5 9 4 8 3 7 y
Rule n
7  4
8  4
Subtract 4 from n.
9  4
10  4
The function y = n – 4 describes this sequence.

16. Additional Example 3: Using Functions to Extend Sequences
Holli keeps a list showing her cumulative earnings for walking her neighbor’s dog. She recorded $1.25 the first time she walked the dog, $2.50 the second time, $3.75 the third time, and $5.00 the fourth time. Write a function that describes the sequence, and then use the function to predict her earnings after 9 walks.
Write the number of walks she recorded; 1.25, 2.50, 3.75, 5.00.
Make a function table.

17. Additional Example 3 Continued
5.00 4
3.75 3
2.50 2
1.25 1 y
Rule n
1 • 1.25
Multiply n by 1.25.
2 • 1.25
3 • 1.25
4 • 1.25
Write the function.
y = 1.25n
9 walks correspond to n = 9. When n = 9, y = 1.25 • 9 = Holli would earn $11.25 after 9 walks.

18. Check It Out: Example 3
Jeff keeps a list showing his cumulative earnings for washing cars. He recorded $2.50 the first time he washed a car, $5 the second time, $7.50 the third time, and $10 the fourth time. Write a function that describes the sequence, and then use the function to predict his earnings after 8 car washes.
Write the number of car washed he recorded; 2.50, 5.00, 7.50,
Make a function table.

19. Check It Out: Example 3 Continued
10.00 4
7.50 3
5.00 2
2.50 1 y
Rule n
1 • 2.50
Multiply n by 1.25.
2 • 2.50
3 • 2.50
4 • 2.50
Write the function.
y = 2.50n
8 car washed correspond to n = 8. When n = 8, y = 2.50 • 8 = 20. Jeff would earn $20. after 8 car washes.

20. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

21. Lesson Quiz: Part I
Tell whether each sequence of y-values is arithmetic or geometric. Write a function that describes each sequence, and then find y when n = 5.
1. 6, 12, 18, 24,…
2. –3, –2, –1, 0,…
3. 24, 21, 18, 15,…
geometric; y = 6n; 30
arithmetic; y = n – 4; 1
arithmetic; y = 27 – 3n; 12

22. Lesson Quiz: Part II
4. Arisha used 0.5 cups of nuts in the first batch of cookies that she made, 1 cup in the second, 1.5 cups in the third, and 2 cups in the fourth. Write a function to describe the sequence, and then use the function to predict the amount of nuts in the seventh batch of cookies.
y = 0.5n; 3.5 cups.

23. Lesson Quiz for Student Response Systems
1. Tell whether the given sequence of y-values is arithmetic or geometric. Identify a function that describes the sequence, and then find y when n = 5.
4, 8, 12, 16, …
A. arithmetic; y = 4n; 20
B. geometric; y = 2n; 10
C. arithmetic; y = 4 + n; 9
D. arithmetic; y = 2n + 2; 12

24. Lesson Quiz for Student Response Systems
2. Tell whether the given sequence of y-values is arithmetic or geometric. Identify a function that describes the sequence, and then find y when n = 5.
–5, –4, –3, –2, …
A. arithmetic; y = n + 6; 11
B. geometric; y = 2n – 6; 4
C. arithmetic; y = n – 6; –1
D. geometric; y = n; 5

25. Lesson Quiz for Student Response Systems
3. Tell whether the given sequence of y-values is arithmetic or geometric. Identify a function that describes the sequence, and then find y when n = 5.
16, 12, 8, 4, …
A. arithmetic; y = 20 – 2n; 10
B. geometric; y = 4n; 20
C. arithmetic; y = 20 – 4n; 0
D. geometric; y = 30 – 6n; 0

26. Lesson Quiz for Student Response Systems
4. Rita used 2 tablespoons of butter for the first recipe, 4 tablespoons for the second, 6 tablespoons for the third, and tablespoons for the fourth. Write a function to describe the sequence, and then use the function to predict the amount of butter in the sixth recipe.
A. y = 2n; 12 tablespoons
B. y = 3n; 18 tablespoons
C. y = 4n; 24 tablespoons
D. y = 2n + 10; 22 tablespoons