# Integrated 1

```Notes: Arithmetic Sequences
Integrated 1, Section 1-5
Name:
Slide 2
Learning Target
Functions Target 2b I can determine if a sequence is an arithmetic sequence.
Given an example of a sequence.
Slide 3
Launch
What do the L(x) and b(x) sequences have in common?
5
Slide 5
Slide 6
Write down everything you know about these tables
C(n) and D(n).
input
output
input
output
1
8
4
5
2
11
5
8
3
14
6
11
4
17
7
14
5
20
8
17
6
23
9
20
input
output
1
8
2
11
3
14
4
17
5
20
6
23
Write down everything you know about these representations L(x) and
C(n).
Slide 7
Arithmetic Sequences
These are arithmetic sequences
•L(n)
3, 5, 7, 9, 11, …
•b(n)
4, 6, 8, 10,12, …
•C(n)
8, 11, 14, 17, 20, …
•D(n)
5, 8, 11, 14, 17, …
Write your definition of an arithmetic sequence.
Slide 8
R(n) 3, 10, 17, ….
What is the first term, R(1)?
What is the 4th term, R(4)?
What is the 11th term, R(11)?
Describe how you found the 11th term in the sequence?
How are the terms generated?
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Page 1 of 3
Integrated 1, Section 1-5
Notes: Arithmetic Sequences
Slide 9
R(n) 3, 10, 17, ….
In this sequence, when you subtract a term from the next term, you always get
____.
Slide 10
____ is the _______________________________________ in this sequence.
Write an equation that can be used to find a term in the sequence when you
know the term that came before it, R(n).
th
Write an equation that can be used to find the n term in the sequence, R(n).
Slide 11
Slide 12
Slide 13
The equation that can be used to find a term in the sequence when you know the
term that came before it, R(n), is:
R(n) = ___________________+ __________________________________
This is called a recursive equation.
th
The equation that can be used to find the n term in the sequence.
R(n) = ___________________+ ________________________________________________
Slide 14
Slide 15
This is called an explicit equation.
Is the sequence, R(n)
3, 10, 17, ….
a function?
If it is, what’s the input? the output?
Slide 16
Slide 17
Team Practice
For each sequence
Find the 4th term in the
sequence.
Find the 11th term in the
sequence.
Write an equation that can
be used to find the nth term
in the sequence.
7, 12, 17, ….
27, 23, 19, …
I’m thinking of a new sequence.
The 4th term in the sequence is 27.
The 10th term in the sequence is 51.
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Integrated 1, Section 1-5
Notes: Arithmetic Sequences
•Find the common difference.
•Find the first term in the sequence.
•Find the equation of the arithmetic sequence.
Slide 18
Team Practice
A new sequence
T(11) = 42 T(21) = 77
Find T(1)
Find T(x)
Slide 19
Debrief
Are arithmetic sequences functions?
How do you know?
Slide 20
Did you hit the target?
I can find the equation or specific terms of an arithmetic sequence.
Slide 21
Rate your understanding of the target from 1 to 5.
Practice
Practice 1.5A Arithmetic Sequences
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