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Splash Screen. Five-Minute Check (over Lesson 8–1) Then/Now New Vocabulary Example 1: Describe an Arithmetic Sequence Example 2: Find a Term in an Arithmetic Sequence Example 3: Real-World Example: Find a Term in an Arithmetic Sequence. Lesson Menu.
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Five-Minute Check (over Lesson 8–1) Then/Now New Vocabulary Example 1: Describe an Arithmetic Sequence Example 2: Find a Term in an ArithmeticSequence Example 3: Real-World Example: Find a Term inan Arithmetic Sequence Lesson Menu
Determine whether the relation {(–2, 2), (0, 1), (–2, 3), (4, 5)} is a function. A. yes B. no • A • B 5-Minute Check 1
Determine whether the relation {(4, –4), (–4, 4), (5, –5), (–5, 5), (1, 5)} is a function. A. yes B. no • A • B 5-Minute Check 2
Determine whether the relation shown in the table is a function. A. yes B. no • A • B 5-Minute Check 3
Determine whether the relation shown in the graph is a function. A. yes B. no 5-Minute Check 4
Let f(x) = 30 ÷ x. Find f(6). A. 3 B. 5 C. 6 D. 24 5-Minute Check 5
You have already used variables to represent patterns. (Lesson 1–2) • Describe sequences using words and symbols. • Find terms of arithmetic sequences. Then/Now
sequence • term • arithmetic sequence • common difference Vocabulary
A. Describe the sequence 15, 16, 17, 18, … using words and symbols. Describe an Arithmetic Sequence The difference of term numbers is 1. The common difference of the terms is 1. Example 1A
The terms have a common difference of 1. A term is 14 more than the term number. Describe an Arithmetic Sequence Answer: So, the equation that describes the sequence is t = n + 14. Example 1A
B. Describe the sequence 10, 20, 30, 40, … using words and symbols. Describe an Arithmetic Sequence The difference of term numbers is 1. The common difference of the terms is 10. Example 1B
The terms have a common difference of 10. A term is 10 times the term number. Describe an Arithmetic Sequence Answer: So, the equation that describes the sequence is t = 10n. Example 1B
A. Describe the sequence 7, 14, 21, 28, … using words and symbols. A. difference of term numbers: 7; common difference: 1; equation: t = n + 3 B. difference of term numbers: 7; common difference: 1; equation: t = 7n C. difference of term numbers: 1; common difference: 7; equation: t = n + 3 D. difference of term numbers: 1; common difference: 7; equation: t = 7n Example 1A
B. Describe the sequence 5, 6, 7, 8, … using words and symbols. A. difference of term numbers: 1; common difference: 5; equation: t = n + 5 B. difference of term numbers: 1; common difference: 1; equation: t = n + 4 C. difference of term numbers: 1; common difference: 4; equation: t = 4n D. difference of term numbers: 5; common difference: 1; equation: t = 5n Example 1B
Write an equation that describes the sequence 6, 9, 12, 15, … . Then find the 11th term of the sequence. Find a Term in an Arithmetic Sequence The difference of the term numbers is 1. The terms have a common difference of 3. The common difference is 3 times the difference of the term numbers. This suggests that t + 3n. However, you need to add 3 to get the exact value of t. Thus, t = 3n + 3. Example 2
CheckIf n = 2, then t = 3(2) + 3 or 9. Find a Term in an Arithmetic Sequence • If n = 4, then t = 3(4) + 3 or 15. To find the 11th term in the sequence, let n = 11 and solve for t. t = 3n + 3 Write the equation. = 3(11) + 3 or 36 Replace n with 11. Answer: The equation t = 3n + 3 describes the sequence. The 11th term is 36. Example 2
Find the 14th term of 4, 9, 14, 19, … . • 19 • 50 • 20 • 69 Example 2
TELEPHONE CHARGES For a telephone call to India, a telephone company charges $8 for the first minute and $4 for each additional minute. How much does it cost for a 10-minute call? Find a Term in an Arithmetic Sequence Example 3
Find a Term in an Arithmetic Sequence Make a table to organize the sequence and find a rule. The difference of the term numbers is 1. The terms have a common difference of 4. The pattern in the table shows the equation c = 4m + 4. c = 4m + 4 Write the equation. = 4(10) + 4 Replace m with 4. = 44 Simplify. Answer: A 10-minute call would cost $44. Example 3
READING During one month Mitch read 3 books. Each month after, he read only 2 books. After 12 months, how many books did Mitch read? • 22 books • 24 books • 25 books • 27 books Example 3