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2. Lesson Menu Five-Minute Check (over Chapter 8) Main Idea and Vocabulary Example 1:Identify Arithmetic Sequences Example 2:Describe an Arithmetic Sequence Example 3:Real-World Example Example 4:Test Example

3. Main Idea/Vocabulary sequence term arithmetic sequence common difference Write algebraic expressions to determine any term in an arithmetic sequence.

4. Example 1 Identify Arithmetic Sequences State whether the sequence 23, 15, 7, –1, –9, … is arithmetic. If it is, state the common difference. Write the next three terms of the sequence. The terms have a common difference of –8, so the sequence is arithmetic. 23, 15, 7, –1, –9Notice that 15 – 23 = –8, 7 – 15 = –8, and so on. –8 Continue the pattern to find the next three terms. Answer: The next three terms are –17, –25, and –33. –9, –17, –25, –33 –8

5. 1.A 2.B 3.C 4.D Example 1 State whether the sequence 29, 27, 25, 23, 21, … is arithmetic. If it is, state the common difference. Write the next three terms of the sequence. A.arithmetic; –2; 19, 17, 15 B.arithmetic; 2; 23, 25, 27 C.arithmetic; –3; 18, 15, 12 D.not arithmetic

6. Example 2 Describe an Arithmetic Sequence Write an expression that can be used to find the nth term of the sequence 0.6, 1.2, 1.8, 2.4, …. Then write the next three terms of the sequence. Use a table to examine the sequence. Answer: An expression that can be used to find the nth term is 0.6n. The next three terms are 0.6(5) or 3, 0.6(6) or 3.6, and 0.6(7) or 4.2. The terms have a common difference of 0.6. Also, each term is 0.6 times its term number.

7. 1.A 2.B 3.C 4.D Example 2 Write an expression that can be used to find the nth term of the sequence 1.5, 3, 4.5, 6, …. Then write the next three terms. A.1.5n; 6.5, 7, 8.5 B.1.5n; 7.5, 9, 10.5 C.0.5n; 6.5, 7, 7.5 D.2.5n; 8.5, 11, 13.5

8. Example 3 TRANSPORTATION This arithmetic sequence shows the cost of a taxi ride for 1, 2, 3, and 4 miles. What would be the cost of a 9-mile ride? The common difference between the costs is 1.75. This implies that the expression for the nth mile is 1.75n. Compare each cost to the value of 1.75n for each number of miles. +1 +1.75

9. Example 3 Each cost is 3.50 more than 1.75n. So, the expression 1.75n + 3.50 is the cost of a taxi ride for n miles. To find the cost of a 9-mile ride, let c represent the cost. Then write and solve an equation for n = 9.

10. Example 3 c = 1.75n + 3.50Write the equation. c = 1.75(9) + 3.50Replace n with 9. c = 15.75 + 3.50 or 19.25Simplify. Answer: It would cost $19.25 for a 9-mile taxi ride.

11. 1.A 2.B 3.C 4.D Example 3 A.$18.75B.$21.50 C.$24.50D.$27.00 TRANSPORTATION This arithmetic sequence shows the cost of a taxi ride for 1, 2, 3, and 4 miles. What would be the cost of a 15-mile ride?

12. Example 4 Which expression can be used to find the nth term in the following arithmetic sequence, where n represents a number’s position in the sequence? A. n + 3 B. 3n C. 2n + 1 D. 3n – 1

13. Example 4 Read the Item You need to find an expression to describe any term. Solve the Item The terms have a common difference of 3 for every increase in position number. So, the expression contains 3n. Answer: D Eliminate choices A and C because they do not contain 3n. Eliminate choice B because 3(1) ≠ 2. The expression in choice D is correct for all the listed terms. So the correct answer is D.

14. 1.A 2.B 3.C 4.D Example 4 A.7n B.4n – 3 C.7 – n D.4n + 3 Let n represent the position of a number in the sequence 7, 11, 15, 19, … Which expression can be used to find any term in the sequence?

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16. Resources Five-Minute Check (over Chapter 8) Image Bank Math Tools Slope and Intercept

17. 1.A 2.B 3.C 4.D Five Minute Check 1 Solve 4m + 5 = 25. Then check your solution. (over Chapter 8) A. B. C. D.

18. 1.A 2.B 3.C 4.D Five Minute Check 2 (over Chapter 8) A.27 B.31 C.35 D.39

19. 1.A 2.B 3.C 4.D Five Minute Check 3 Solve the inequality –2x ≤ 5. Then check your solution. (over Chapter 8) A. B. C. D.

20. 1.A 2.B 3.C 4.D Five Minute Check 4 A.a < –9 B.a > –9 C.a > 9 D.a < 9 Solve the inequality a + 2 > –7. Then check your solution. (over Chapter 8)

21. 1.A 2.B 3.C 4.D Five Minute Check 5 A.5x – 4 > 19 B.5x – 4 < 19 C.5x + 4 < 19 D.5x + 4 > 19 Translate four less than five times a number is greater than nineteen into an inequality. (over Chapter 8)

22. 1.A 2.B 3.C 4.D Five Minute Check 6 A.x > 9 B.x ≤ 4 C.x ≥ 9 D.x ≥ 4 The perimeter of a square with side length x is no less than 36 inches. Which inequality represents all possible values for x? (over Chapter 8)

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