Algebra 2 Note-taking Guide
Algebra 2 - Lesson 8.01 Arithmetic Sequences
Please print this out in advance, and as you are working through the lesson, fill in the information and use this as your notes.
 The goal is to have all the empty boxes checked
Use this set of arrows
to guide you through
the lesson
As you complete this lesson, please check that you can answer:
 How can an expression or a process be determined for an arithmetic sequence?
 What functions combine to create an explicit formula for arithmetic sequences?
 What possible restrictions exist on domains and ranges of arithmetic sequences?
Arithmetic Sequences (page 1)
An arithmetic sequence is a list of numbers, called terms, which share a common ___________________.
Complete the sorting activity on page 1 to separate the arithmetic sequences from the non-arithmetic sequences
and record the correct answers in the chart below:
Arithmetic Sequence
Non-Arithmetic Sequence
Different Forms (page 2)
A sequence can appear in multiple forms.
The most common is a list of terms; however, other ways to display the data, like a table or a graph, may also be
used.
Algebra 2 Notetaking Guide
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Florida Virtual School
Fill in the table below with the different forms to represent the sequence on page 2:
List
Table
n
Graph
f(n)
Important Note
You will notice on the graph that there is not a continuous line through the points. That is because a sequence is
a _______________ set of points. This means that the sequence only exists at those points. That is different from a
graph of a line which is a continuous set of points.
Recursive Versus Explicit (page 2)
Fill in the table below to illustrate the difference between recursive and explicit processes.
Recursive
A recursive process requires the use of the previous term in a sequence.
Explicit
An explicit formula allows you to calculate any term in a sequence directly.
Algebra 2 Notetaking Guide
Version 14
Florida Virtual School
Arithmetic Sequence Formula (page 2)
What does each of the variables mean?
Use this space to record the steps for applying the arithmetic
sequence formula to the sequence 2, 9, 16, …
𝑎1 = _______________________________________________
𝑑 = ________________________________________________
(𝑛 − 1) = _________________________________________
𝑎𝑛 = _______________________________________________
Converting Recursive and Explicit Equations (page 2)
Combination of Functions (page 3)
One way to think of the explicit formula is as a combination of functions or two separate parts.
Algebra 2 Notetaking Guide
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Florida Virtual School
Domain and Range (page 3)
Domain:
Range:
Use the space below to complete examples 1 and 2:
Example 1:
Example 2:
Identify the 46th term of an arithmetic sequence where
a1 = −22 and a12 = 77.
There is a library containing triangular bookshelves
where each consecutive shelf contains 4 more books
than the shelf above it. If the top shelf holds 7 books,
how many books are on the 11th shelf?
Be sure to look at an additional example in this section:
Algebra 2 Notetaking Guide
Version 14
Florida Virtual School
Practice (page 4)
Finally, complete the 8.01 Assessment, Arithmetic Sequences. This is an auto-graded assignment. You will get
immediate feedback on your work.
Algebra 2 Notetaking Guide
Version 14
Florida Virtual School