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5-Minute Check 1

A B. Determine whether the relation {(–2, 2), (0, 1), (–2, 3), (4, 5)} is a function. Determine whether the relation shown in the table is a function. A B. Let f ( x ) = 30 ÷ x . Find f (6). 5-Minute Check 1. Splash Screen.

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5-Minute Check 1

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  1. A B Determine whether the relation {(–2, 2), (0, 1), (–2, 3), (4, 5)} is a function. Determine whether the relation shown in the table is a function. • A • B Let f(x) = 30 ÷ x. Find f(6). 5-Minute Check 1

  2. Splash Screen

  3. You have already used variables to represent patterns. (Lesson 1–2) • Describe sequences using words and symbols. • Find terms of arithmetic sequences. Then/Now

  4. sequence An ordered list of numbers, such as, 0, 1, 2, 3 or 2, 4, 6, 8 • term • arithmetic sequence • common difference Each number within a sequence is called a term A sequence in which the difference between any two consecutive terms is the same The difference between any two consecutive terms in an arithmetic sequence Vocabulary

  5. 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

  6. 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

  7. 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

  8. 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

  9. A B C D 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

  10. A B C D 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

  11. 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

  12. 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

  13. A B C D Find the 14th term of 4, 9, 14, 19, … . • 19 • 50 • 20 • 69 Example 2

  14. 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

  15. 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 10. = 44 Simplify. Answer: A 10-minute call would cost $44. Example 3

  16. A B C D 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

  17. End of the Lesson

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