Arithmetic Sequence as a Table

Lesson 1.5 Exploring
Arithmetic Sequences

Obj: 12C: I can find terms in arithmetic sequences.

12D: I can write explicit and recursive arithmetic

sequence formulas.

EQ: How can I write a rule for arithmetic patterns?

Roles:
Facilitator:
Scribe
Resourcer
Includer

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Communicates conflicts or questions to the teacher.

Poll

What role do you plan to play today?

• Facilitator

• Scribe

• Resourcer

• Includer

Warm Up

Part 1: Introducing Sequence Notation

A restaurant has square tables that can seat 4 people, one on each side of the table. For larger parties, the restaurant will frequently push table together in a side-by-side fashion, creating a longer table. How many people can be seated when 2 tables are used? 3 tables? 10 tables?

The tables should look something like this

Tables

1

2

3

4

5

…

10

People

…

Is it Arithmetic?

Does the sequence of number of people
{4, 6, 8, 10, 12, …} meet the definition of
an arithmetic sequence? If it does, what is
the common difference?

Word Cloud

What makes a sequence an arithmetic sequence?

Part 2: Applying Sequence Notation in Problem Solving

Odeon of Herodes Atticus is an ancient
amphitheater in Athens, Greece.It was
built in 161 and seats 6,000 people.

If we knew how many seats there were
in the 1st row, and we knew the number
of seats in each row increased by a
constant amount, would it be possible to
find the number of seats in the 20th row
without actually counting seats?

Suppose the theater has 200 seats in the 1st row and
every row adds 50 seats. Can you write an arithmetic
sequence to keep track of the number of seats in each
row?

Find the number of seats in the 6th row.

Describe how to find the # of seats in the nth row.

Fill in the Blanks

Suppose the theater has 200 seats in the 1st row and
every row adds 50 seats. How many seats in the 6th row?

Multiple Select

Suppose the theater has 200 seats in the 1st row and
every row adds 50 seats. Which of the following could represent the nth row?

• a(n)=200+50(n-1)

• a(n)=50+200(n-1)

• a(n)=50n+150

• a(n)=200n-150

Part 3: Summary and Practice

In your journal, write out the table with verbal descriptions, symbolic notations, and examples.

Explicit Arithmetic Sequence Formula
a(n) = a_(k) + d(n - k)

a_(k) is the kth term

d is the common difference

n is a term

a(n) is the nth term

​k is another term

Fill in the Blanks

What's the common difference of x_n?

Fill in the Blanks

What's x₈?

Fill in the Blanks

What's x₁₂?

Multiple Choice

What's the common difference of a_m?

• -13

• 1

• -1

• -13

Multiple Choice

What's a₁₂?

• -13

• 52

• 65

• 39

• 0

Multiple Choice

What's a₁₅?

• -13

• 52

• 65

• 39

• 0

Multiple Choice

Suppose you are given an arithmetic sequence whose first term is x₁ = 53 and that has a common difference of -4. What are the next 3 terms in the sequence?

• 49, 45, 41
• 45, 41, 37
• 53, 49, 45
• 57, 61, 65
• 53, 57, 61

Fill in the Blanks

Suppose you are given an arithmetic sequence whose first term is x₁ = 53 and that has a common difference of -4. What is the value of the 12th term?

Multiple Choice

A grocery store worker has to collect all the shopping carts left out in the parking lot. He measures the 4 carts he collected to be 51 inches. He collects another cart for a total of 5 carts and measures the length to be 57 inches. He counts 21 carts in the parking lot. How long is this?

• 153 inches

• 163 inches

• 171 inches

Multiple Choice

If he is pushing a line of carts that is 117 inches long, how many carts does he have?

• 7 carts

• 8 carts

• 15 carts

• 19 carts

• 13 carts

Fill in the Blanks

How long is a single cart (in inches)?

Multiple Choice

How much MB of available storage is being filled by the movie per minute?

• 60 MB/min

• 60 min/MB

• 240 MB/min

• 240 min/MB

Multiple Choice

How much MB was available on her phone before the download started?

• 240 MB

• 548 MB
• 2,525 MB

• 4,450 MB

Fill in the Blanks

Suppose the download lasted 19 minutes. How much storage is available after the download is finished?

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.

● Go to your calendar paper.

● Select a skill to work on independently or with a partner.

● Work on Unit 1 Deltamath.

Self-Acquisition Time