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Lesson Menu. 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.

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Lesson menu

Lesson Menu

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


Main idea vocabulary

  • Translate information in tables to expressions.

  • sequence

  • term

  • arithmetic sequence

  • common difference

Main Idea/Vocabulary


Ngsss

MA.8.A.1.1Create 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.1.5Translate among verbal, tabular,graphicaland algebraic representations of linear functions.

NGSSS


Example 1

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


Example 11

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


Example 1 cyp

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


Example 2

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


Example 21

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


Example 2 cyp

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


Example 3

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


Example 31

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.

Answer: The expression is 1.75m + 3.50.

Example 3


Example 3 cyp

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

Example 3 CYP


Example 4

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


Example 41

Use a Table to Analyze a Sequence

Evaluate the expression when m = 9.

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

=15.75 + 3.50Multiply 1.75 and 9.

=19.25Simplify.

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

Example 4


Example 4 cyp

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


Five minute check 1

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

Five Minute Check 1


Five minute check 2

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

Five Minute Check 2


Five minute check 3

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

Five Minute Check 3


Five minute check 4

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

Five Minute Check 4


Five minute check 5

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

Five Minute Check 5


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