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 Lesson Menu

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

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. NGSSS

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

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

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

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

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

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

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

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

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

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

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. Answer: It will cost $19.25 for a 9-mile ride. Example 4

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

Write an expression that can be used to find the nth term 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

Write an expression that can be used to find the nth term of the sequence. Then use the expression to find 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

Write an expression to find the nth term of the arithmetic sequence 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

Write an expression to find the nth term of the arithmetic sequence 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

Chris earns $480 per week in a sales position 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