Lesson 10-4

Example 1 Identify Arithmetic Sequences
State whether the sequence 11, 8, 5, 2, –1, … is arithmetic. If it is, state the common difference and write the next three terms.

11,	8,	5,	2,	–1	Notice that 8 – 11 = –3, 5 – 8 = –3, and so on.

     – 3	     – 3	     – 3	     – 3

The terms have a common difference of –3, so the sequence is arithmetic. Continue the pattern to find the next three terms.
–1,	–4,	–7,	–10		The next three terms are –4, –7, and –10.

      – 3	       – 3	       – 3

Example 2 Describe an Arithmetic Sequence
Write an expression that can be used to find the nth term of the sequence
3, 5, 7, 9, …. Then write the next three terms.

+1

+1

+1

Use a table to example the sequence.					                
Term Number (n)	1	2	3	4	
Term	3	6	9	12	

+3

+3

+3

The terms have a common difference of 3.			 	        
Also, each term is 3 times its term number.
An expression that can be used to find the
nth term is 3n.

The next three terms are 3(5) or 15, 3(6) or 18, and 3(7) or 21.

Example 3 Real-World Example
RENTAL The table shows the cost of renting a motorized scooter for different numbers of hours. How much would it cost to rent a scooter for 8 hours?

Hours	Cost ($)	
1	7.50	
2	10.00	
3	12.50	
4	15.00	

The common difference between the costs is 2.50. This implies that the expression for the nth day is 2.50n. Compare each cost to the value of 2.50n for each number of days.

Hours	Cost ($)	2.50n	
1	7.50	2.50	
2	10.00	5.00	
3	12.50	7.50	
4	15.00	10.00	
Each cost is 5 more than 2.50n. So, the expression 2.50n + 5 is the cost of renting a scooter for n hours. To find the cost of renting a scooter for 8 hours, let c represent the cost. Then write and solve an equation for n = 8.

c = 2.50n + 5		Write the equation.
c = 2.50(8) + 5		Replace n with 8.
c = 20 + 5 or 25	Simplify.

It would cost $25 to rent a scooter for 8 hours.

Example 4 STANDARDIZED TEST PRACTICE EXAMPLE
Which expression can be used to find the nth term in the following sequence, where n represents a number’s position in the sequence?

Position in Sequence	1	2	3	4	n	
Term	4	7	10	13	?	

A  n + 3	B  3n		C  4n – 1		D  3n + 1

Read the Test Item You need to find an expression to describe any term.

Solve the Test Item The terms have a common difference of 3 for every increase in positive number. So the expression contains 3n.
•	Eliminate choices A and C because they do not contain 3n.
•	Eliminate choice B because 3(1)  4.
•	The expression in choice D is correct for all the listed terms. So the correct answer is D.