Download 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.
Determine whether the relation
shown in the table is a function.
Let f(x) = 30 ÷ x. Find f(6).
1.
2.
A. A
B. B
A
B
You have already used variables to represent
patterns. (Lesson 1–2)
• Describe sequences using words and
symbols.
• Find terms of arithmetic sequences.
• sequence
• term
An ordered list of numbers, such as, 0, 1, 2, 3 or 2, 4, 6, 8
Each number within a sequence is called a term
• arithmetic sequence
• common difference
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
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
A.
B.
C.
D.
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
A.
B.
C.
D.
A
B
C
D
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
A.
B.
C.
D.
A
B
C
D
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 10.
= 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
A.
B.
C.
D.
A
B
C
D