Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–1) Then/Now New Vocabulary Example 1:Describe an Arithmetic Sequence Example 2: Find a Term.

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Splash Screen

Lesson Menu 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

Over Lesson 8–1 A.A B.B 5-Minute Check 1 A.yes B.no Determine whether the relation {(–2, 2), (0, 1), (–2, 3), (4, 5)} is a function.

Over Lesson 8–1 A.A B.B 5-Minute Check 2 A.yes B.no Determine whether the relation {(4, –4), (–4, 4), (5, –5), (–5, 5), (1, 5)} is a function.

Over Lesson 8–1 A.A B.B 5-Minute Check 3 Determine whether the relation shown in the table is a function. A.yes B.no

Over Lesson 8–1 5-Minute Check 4 A.yes B.no Determine whether the relation shown in the graph is a function.

Over Lesson 8–1 5-Minute Check 5 A.3 B.5 C.6 D.24 Let f(x) = 30 ÷ x. Find f(6).

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

Vocabulary sequence term arithmetic sequence common difference

Example 1A Describe an Arithmetic Sequence A. Describe the sequence 15, 16, 17, 18, … using words and symbols. The common difference of the terms is 1. The difference of term numbers is 1.

Example 1A Describe an Arithmetic Sequence Answer: So, the equation that describes the sequence is t = n The terms have a common difference of 1. A term is 14 more than the term number.

Example 1B Describe an Arithmetic Sequence B. Describe the sequence 10, 20, 30, 40, … using words and symbols. The common difference of the terms is 10. The difference of term numbers is 1.

Example 1B Describe an Arithmetic Sequence Answer: So, the equation that describes the sequence is t = 10n. The terms have a common difference of 10. A term is 10 times the term number.

Example 1A 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 1B 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 2 Find a Term in an Arithmetic Sequence 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. The difference of the term numbers is 1. The terms have a common difference of 3. Write an equation that describes the sequence 6, 9, 12, 15, …. Then find the 11th term of the sequence.

Example 2 Find a Term in an Arithmetic Sequence CheckIf n = 2, then t = 3(2) + 3 or 9. To find the 11th term in the sequence, let n = 11 and solve for t. t=3n + 3Write the equation. =3(11) + 3 or 36Replace n with 11. If n = 4, then t = 3(4) + 3 or 15. 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, …. A.19 B.50 C.20 D.69

Example 3 Find a Term in an Arithmetic Sequence 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?

Example 3 Find a Term in an Arithmetic Sequence Make a table to organize the sequence and find a rule. The pattern in the table shows the equation c = 4m + 4. c =4m + 4Write the equation. =4(10) + 4Replace m with 4. =44Simplify. The difference of the term numbers is 1. The terms have a common difference of 4. 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? A.22 books B.24 books C.25 books D.27 books

End of the Lesson