2. Main Idea and New Vocabulary
Example 1: Use a Table to Analyze a Sequence
Example 2: Use a Table to Analyze a Sequence
Example 3: Real-World Example: Use a Table to Analyze a Sequence
Example 4: Real-World Example: Use a Table to Analyze a Sequence
Lesson Menu

3. Translate information in tables to expressions.
sequence
term
arithmetic sequence
common difference
Main Idea/Vocabulary

4. Use a Table to Analyze a Sequence
Use a table to write an expression that can be used to find the nth term of the sequence 6, 12, 18, 24, …. Then use the expression to find the next three terms.
Make a table to analyze the pattern.
The terms have a common difference of 6. Also, each term is 6 times its term number.
Example 1

5. Use a Table to Analyze a Sequence
An expression that can be used to find the nth term is 6n.
The next three terms are 6(5) or 30, 6(6) or 36, and 6(7) or 42.
Answer: 6n; 30, 36, 42
Example 1

6. Use a table to write an expression that can be used to find the nth term of the sequence 8, 16, 24, 32, …. Then use the expression to find the next three terms.
A. 4n; 36, 40, 44
B. 6n; 36, 42, 48
C. 8n; 40, 48, 56
D. 12n; 36, 48, 60
Example 1 CYP

7. Use a Table to Analyze a Sequence
Use a table to write an expression that can be used to find the nth term of the sequence 3, 7, 11, 15, …. Then use the expression to find the next three terms.
The terms have a common difference of 4. Start with 4n. Then subtract 1 to get the term. So, the expression to find the nth term is 4n – 1.
Example 2

8. Use a Table to Analyze a Sequence
The next three terms are 4(5) – 1 or 19, 4(6) – 1 or 23, and 4(7) – 1 or 27.
Answer: 4n – 1; 19, 23, 27
Example 2

9. Use a table to write an expression that can be used to find the nth term of the sequence 7, 10, 13, 16, …. Then use the expression to find the next three terms.
A. 3n + 4; 19, 22, 25
B. 3n – 4; 11, 14, 17
C. 4n + 3; 23, 27, 31
D. 4n – 3; 17, 21, 25
Example 2 CYP

10. Use a Table to Analyze a Sequence
TRANSPORTATION The table shows the cost of a taxi ride for 1, 2, 3, and 4 miles. Write an expression that can be used to find the total cost for m miles.
Example 3

11. Use a Table to Analyze a Sequence
The common difference between the costs is Start with 1.75m. Then add $3.50 to get the total cost.
Answer: The expression is 1.75m
Example 3

12. JET SKIS The table shows the cost for renting a water jet ski for 1, 2, 3, and 4 hours. Write an expression that can be used to find the total cost for h hours.
A h + 25
B h + 20
C. 20h
D. 25h
Example 3 CYP

13. Use a Table to Analyze a Sequence
TRANSPORTATION The table shows the cost of a taxi ride for 1, 2, 3, and 4 miles. What would be the cost of a 9-mile ride?
Example 4

14. Use a Table to Analyze a Sequence
Evaluate the expression when m = 9.
1.75m = 1.75(9) Replace m with 9.
= Multiply 1.75 and 9.
= Simplify.
Answer: It will cost $19.25 for a 9-mile ride.
Example 4

15. JET SKIS The table shows the cost for renting a water jet ski for 1, 2, 3, and 4 hours. What would be the cost to rent a jet ski for 6 hours?
A. $112
B. $137.50
C. $139.50
D. $164.50
Example 4 CYP