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

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

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

Determine whether the relation shown in the table is a function.

A. yes

B. no

Over Lesson 8–1

A. yes

B. no

Determine whether the relation shown in the graph is a function.

Over Lesson 8–1

A. 3

B. 5

C. 6

D. 24

Let f(x) = 30 ÷ x. Find f(6).

You have already used variables to represent patterns. (Lesson 1–2)

• Describe sequences using words and symbols.

• Find terms of arithmetic sequences.

• sequence

• term

• arithmetic sequence

• common difference

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.

Describe an Arithmetic Sequence

Answer: So, the equation that describes the sequence is t = n + 14.

The terms have a common difference of 1. A term is 14 more than the term number.

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.

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.

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

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

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.

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 + 3 Write the equation.

= 3(11) + 3 or 36 Replace 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.

Find the 14th term of 4, 9, 14, 19, … .

A. 19

B. 50

C. 20

D. 69

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?

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 + 4 Write the equation.

= 4(10) + 4 Replace m with 4.

= 44 Simplify.

The difference of the term numbers is 1.

The terms have a common difference of 4.

Answer: A 10-minute call would cost $44.

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