Main Idea and New Vocabulary

NGSSS

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

Five-Minute Check

• Translate information in tables to expressions.

• sequence

• term

• arithmetic sequence

• common difference

MA.8.A.1.1 Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data.

MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions.

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.

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.

Use a Table to Analyze a Sequence

Answer: 6n; 30, 36, 42

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

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.

Use a Table to Analyze a Sequence

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.

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

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

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.

Use a Table to Analyze a Sequence

Answer: The expression is 1.75m + 3.50.

Use a Table to Analyze a Sequence

The common difference between the costs is 1.75. Start with 1.75m. Then add $3.50 to get the total cost.

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. 14.50h + 25

B. 19.50h + 20

C. 20h + 19.50

D. 25h + 14.50

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?

Use a Table to Analyze a Sequence

Evaluate the expression when m = 9.

1.75m + 3.50 = 1.75(9) + 3.50 Replace m with 9.

= 15.75 + 3.50 Multiply 1.75 and 9.

= 19.25 Simplify.

Use a Table to Analyze a Sequence

Answer: It will cost $19.25 for a 9-mile ride.

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

Write an expression that can be used to find the nthterm of the sequence. Then use the expression to find the next three terms.

A. n + 2; 13, 15, 17

B. 2n + 1; 11, 13, 15

C. 2n + 3; 13, 15, 17

D. 2n + 3; 14, 17, 20

Write an expression that can be used to find the nthterm of the sequence. Then use the expression tofind the next three terms.

A. –3n; –15, –18, –21

B. 3n; –15, –18, –21

C. n – 3; –15, –18, –21

D. –3n; –36, –108, –324

Write an expression to find the nth term of the arithmetic sequence. Then find the indicated term.3, 8, 13, 18, …, n = 10

A. 5n – 2; 43

B. 5n – 2; 48

C. 3n + 2; 32

D. 3n – 2; 38

Write an expression to find the nth term of the arithmetic sequence. Then find the indicated term.2, –2, –6, –10, …, n = 22

A. –6n + 4; –128

B. –4n – 6; –94

C. –4n + 6; –82

D. n – 4; –18

Chris earns $480 per week in a sales position. Additionally, Chris receives a bonus of $30 for each sale he makes that week. Which algebraic expression shows how much Chris will earn if he makes n sales?

A. 480 + n

B. 30 + 480n

C. 480 – 30n

D. 480 + 30n