Transcript 8-2 Sequences_and_Equations

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
Determine whether the relation
{(–2, 2), (0, 1), (–2, 3), (4, 5)} is a function.
A. yes
B. no
A. A
B. B
Over Lesson 8–1
Determine whether the relation
{(4, –4), (–4, 4), (5, –5), (–5, 5), (1, 5)} is a function.
A. yes
B. no
A. A
B. B
Over Lesson 8–1
Determine whether the relation
shown in the table is a function.
A. yes
B. no
A. A
B. B
Over Lesson 8–1
Determine whether the relation
shown in the graph is a function.
A. yes
B. no
Over Lesson 8–1
Let f(x) = 30 ÷ x. Find f(6).
A. 3
B. 5
C. 6
D. 24
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 difference of term numbers is 1.
The common difference of the terms is 1.
Describe an Arithmetic Sequence
The terms have a common difference of 1. A term is 14
more than the term number.
Answer: So, the equation that describes the
sequence is t = n + 14.
Describe an Arithmetic Sequence
B. Describe the sequence 10, 20, 30, 40, … using
words and symbols.
The difference of term numbers is 1.
The common difference of the terms is 10.
Describe an Arithmetic Sequence
The terms have a common difference of 10. A term
is 10 times the term number.
Answer: So, the equation that describes the
sequence is t = 10n.
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
Write an equation that describes the sequence 6, 9, 12, 15, … .
Then find the 11th term of the 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.
Find a Term in an Arithmetic Sequence
Check
If n = 2, then t = 3(2) + 3 or 9.
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
= 3(11) + 3 or 36
Write the equation.
Replace n with 11.
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 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.
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