(7) Lesson 5.2 - Sequences

1. Evaluate each expression if m = 2, n = 4, r = 7, and p = 9.
1. 2. 7r – 3p
3. (p – m) + 5(2n) 4.
5. Kerrie works at an art supply store. Write an expression
Kerrie could use to find the cost of buying p cases of
paintbrushes at $145 each and e easels at $59 each.
Course 2, Lesson 5-2
2
n
m
2
(13 )
12
r

2. Answers
1. 8
2. 22
3. 47
4. 3
5. 145p + 59e
Course 2, Lesson 5-2

3. HOW can you use numbers and
symbols to represent mathematical
ideas?
Expressions and Equations
Course 2, Lesson 5-2

4. Preparation for:
• 7.EE.1
Apply properties of operations as strategies to add, subtract, factor, and
expand linear expressions with rational coefficients.
• 7.EE.2
Understand that rewriting an expression in different forms in a problem
context can shed light on the problem and how the quantities in it are
related.
Course 2, Lesson 5-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

5. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course 2, Lesson 5-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

6. • To describe and extend sequences
• To write an algebraic expression to
represent a sequence of numbers
Course 2, Lesson 5-2
Expressions and Equations

7. Course 2, Lesson 5-2
Expressions and Equations
• sequence
• term
• arithmetic sequence

8. 1
Need Another Example?
2
Step-by-Step Example
1. Describe the relationship between the terms in the
arithmetic sequence 8, 13, 18, 23, … . Then write the
next three terms in the sequence.
8, 13, 18, 23, … Each term is found by adding
5 to the previous term.
23 + 5 = 28
Continue the pattern to find the next three terms.
The next three terms are 28, 33, and 38.
28 + 5 = 33 33 + 5 = 38

9. Answer
Need Another Example?
Describe the relationship between the terms in
the arithmetic sequence 7, 11, 15, 19, … . Then
write the next three terms in the sequence.
4 is added to each term; 23, 27, 31.

10. 1
Need Another Example?
2
Step-by-Step Example
2. Describe the relationship between the terms in the
arithmetic sequence 0.4, 0.6, 0.8, 1.0, ... . Then write
the next three terms in the sequence.
1.0 + 0.2 = 1.2
Continue the pattern to find the next three terms.
The next three terms are 1.2, 1.4, and 1.6.
1.2 + 0.2 = 1.4 1.4 + 0.2 = 1.6
Each term is found by adding
0.2 to the previous term.
0.4, 0.6, 0.8, 1.0, …

11. Answer
Need Another Example?
Describe the relationship between the terms in
the arithmetic sequence 0.1, 0.5, 0.9, 1.3, … .
Then write the next three terms in the sequence.
Each term is 0.4 greater than the
previous term; 1.7, 2.1, 2.5.

12. 1
Need Another Example?
2
3
Step-by-Step Example
3. The greeting cards that Meredith makes are sold in boxes at a
gift store. The first week, the store sold 5 boxes. Each week,
the store sells five more boxes. The pattern continues. What
algebraic expression can be used to find the total number of
boxes sold at the end of the 100th week? What is the total?
Each term is 5 times its position. So, the expression is 5n.
5n
At the end of 100 weeks, 500 boxes will have been sold.
Write the expression.
Replace n with 100.5(100) = 500

13. Answer
Need Another Example?
Mehmet started a new exercise routine. The first
day, he did 2 sit-ups. Each day after that, he did
2 more sit-ups than the previous day. If he continues
this pattern, what algebraic expression can be used to
help find the total number of sit-ups on the tenth day?
Use the expression to find the number.
2d ; 20 sit-ups.

14. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-2
Expressions and Equations

15. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-2
Expressions and Equations
Sample answers:
• To describe the relationship between the terms in a
sequence
• To write an algebraic expression that represents a
sequence

16. What is the 9th term of the
sequence shown below?
8, 16, 24, 32, …
Course 2, Lesson 5-2
Ratios and Proportional RelationshipsExpressions and Equations