Main Idea and New Vocabulary
NGSSS
Example 1: Use a Table to Analyze a Sequence
Example 2: Use a Table to Analyze a Sequence
Example 3: Real-World Example: Use a Table to
Analyze a Sequence
Example 4: Real-World Example: Use a Table to
Analyze a Sequence
Five-Minute Check
• Translate information in tables to expressions.
• sequence
• term
• arithmetic sequence
• common difference
MA.8.A.1.1 Create and interpret tables,
graphs, and models to represent, analyze,
and solve problems related to linear
equations, including analysis of domain, range
and the difference between discrete and
continuous data.
MA.8.A.1.5 Translate among verbal, tabular,
graphical and algebraic representations of
linear functions.
Use a Table to Analyze a Sequence
Use a table to write an expression that can be
used to find the nth term of the sequence 6, 12,
18, 24, …. Then use the expression to find the
next three terms.
Make a table to analyze the pattern.
The terms have a common difference of 6. Also, each
term is 6 times its term number.
Use a Table to Analyze a Sequence
An expression that can be used to find the nth term
is 6n.
The next three terms are 6(5) or 30, 6(6) or 36, and
6(7) or 42.
Answer: 6n; 30, 36, 42
Use a table to write an expression that can be
used to find the nth term of the sequence 8, 16,
24, 32, …. Then use the expression to find the
next three terms.
A. 4n; 36, 40, 44
B. 6n; 36, 42, 48
C. 8n; 40, 48, 56
D. 12n; 36, 48, 60
Use a Table to Analyze a Sequence
Use a table to write an expression that can be
used to find the nth term of the sequence 3, 7, 11,
15, …. Then use the expression to find the next
three terms.
The terms have a common difference of 4. Start with
4n. Then subtract 1 to get the term. So, the
expression to find the nth term is 4n – 1.
Use a Table to Analyze a Sequence
The next three terms are 4(5) – 1 or 19, 4(6) – 1 or
23, and 4(7) – 1 or 27.
Answer: 4n – 1; 19, 23, 27
Use a table to write an expression that can be
used to find the nth term of the sequence 7, 10,
13, 16, …. Then use the expression to find the
next three terms.
A. 3n + 4; 19, 22, 25
B. 3n – 4; 11, 14, 17
C. 4n + 3; 23, 27, 31
D. 4n – 3; 17, 21, 25
Use a Table to Analyze a
Sequence
TRANSPORTATION The table shows the cost of a
taxi ride for 1, 2, 3, and 4 miles. Write an
expression that can be used to find the total cost
for m miles.
Use a Table to Analyze a
Sequence
The common difference between the costs is 1.75.
Start with 1.75m. Then add $3.50 to get the total
cost.
Answer: The expression is 1.75m + 3.50.
JET SKIS The table shows the cost for renting a
water jet ski for 1, 2, 3, and 4 hours. Write an
expression that can be used to find the total cost
for h hours.
A. 14.50h + 25
B. 19.50h + 20
C. 20h + 19.50
D. 25h + 14.50
Use a Table to Analyze a
Sequence
TRANSPORTATION The table shows the cost of a
taxi ride for 1, 2, 3, and 4 miles. What would be
the cost of a 9-mile ride?
Use a Table to Analyze a
Sequence
Evaluate the expression when m = 9.
1.75m + 3.50 = 1.75(9) + 3.50
Replace m with 9.
= 15.75 + 3.50
Multiply 1.75 and 9.
= 19.25
Simplify.
Answer: It will cost $19.25 for a 9-mile ride.
JET SKIS The table shows the cost for renting a
water jet ski for 1, 2, 3, and 4 hours. What would
be the cost to rent a jet ski for 6 hours?
A. $112
B. $137.50
C. $139.50
D. $164.50
Write an expression that can be used to find the nth
term of the sequence. Then use the expression to
find the next three terms.
A. n + 2; 13, 15, 17
B. 2n + 1; 11, 13, 15
C. 2n + 3; 13, 15, 17
D. 2n + 3; 14, 17, 20
Write an expression that can be used to find the nth
term of the sequence. Then use the expression to
find the next three terms.
A. –3n; –15, –18, –21
B. 3n; –15, –18, –21
C. n – 3; –15, –18, –21
D. –3n; –36, –108, –324
Write an expression to find the nth term of the
arithmetic sequence. Then find the indicated term.
3, 8, 13, 18, …, n = 10
A. 5n – 2; 43
B. 5n – 2; 48
C. 3n + 2; 32
D. 3n – 2; 38
Write an expression to find the nth term of the
arithmetic sequence. Then find the indicated term.
2, –2, –6, –10, …, n = 22
A. –6n + 4; –128
B. –4n – 6; –94
C. –4n + 6; –82
D. n – 4; –18
Chris earns $480 per week in a sales position.
Additionally, Chris receives a bonus of $30 for each
sale he makes that week. Which algebraic expression
shows how much Chris will earn if he makes n sales?
A. 480 + n
B. 30 + 480n
C. 480 – 30n
D. 480 + 30n