
Arithmetic Sequences
Presentation
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Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Medium
Standards-aligned
Teri Salter
Used 274+ times
FREE Resource
8 Slides • 14 Questions
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Arithmetic Sequences
By Teri Salter
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Multiple Choice
Which sequence is NOT an arithmetic sequence?
-7, -13, -19, -25,...
-10, -6, -2, 2,..
6, 8, 10, 12,...
3, 15, 75, 375,...
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Multiple Choice
Which sequence is NOT an arithmetic sequence?
12, 18, 24, 30,...
10, 3, -4, -11,...
2, 4, 8, 16,...
16, 20, 24, 28,...
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Multiple Choice
We will start with the explicit formula. Given the following sequence, state the first term and common difference.
Example 1: 4, 7, 10, 13, 16, …
a1 = 3, d = 4
a1 = 16, d = 3
a1 = 4, d = 3
a1 = 16, d = 13
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Multiple Choice
Now, write the explicit formula for the given sequence.
Example 1: 4, 7, 10, 13, 16, …
an = 4 + (n − 1)(3)
an = 3 + (n − 1)(4)
an = 7 + (n − 1)(3)
an = 16 + (n − 1)(4)
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Fill in the Blanks
Type answer...
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Multiple Choice
Write an explicit rule to model the following sequence:
Example 2: 21, 19, 17, 15, …
an = 21 +(n − 1)(2)
an = −21 +(n − 1)(2)
an = −21 +(n − 1)(−2)
an = 21 +(n − 1)(−2)
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Multiple Choice
Write and explicit rule to model the following sequence:
Example 3: -12, -7, -2, …
an = 5 + (n −1)(−12)
an = −12 + (n −1)(5)
an = −5 + (n −1)(12)
an = 12 + (n −1)(−5)
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Multiple Choice
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Multiple Choice
***What do the three dots (ellipsis) mean at the end of a sequence?***
The sequence starts going in reverse order
The sequence ends
The sequence goes on forever
The sequence increases by one from here on
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Fill in the Blanks
Type answer...
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Multiple Choice
Now, let's go backwards!!! Given the explicit formula, list the first five terms in order.
an = 3 + (n − 1)(2)
2, 5, 8, 11, 14, ...
3, 1, -1, -3, -5, ...
3, 6, 9, 12, 15, ...
3, 5, 7, 9, 11, ...
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Now, let's simplify the explicit formula even further
an = 4 + (n - 1)(-2) **What do you see that we can do to this equation?
Some text here about the topic of discussion
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Now, our equation is an = -2n + 6
an = -2n + 6 **How does this resemble linear equation in slope- intercept form?
y = mx + b Slope-Intercept Form
Some text here about the topic of discussion
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Arithmetic Sequences Model Linear Functions!!!
an = -2n + 6 **The common difference is the same as the slope!
y = mx + b **The y-intercept is the difference of the first term
and the common difference... or b = a1 - d
Some text here about the topic of discussion
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Multiple Choice
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)
an = 6n + 2
an = 6n - 6
an = 6n - 4
an = -6n + 4
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Multiple Choice
22
Multiple Choice
TRUE or FALSE?
An arithmetic sequence is an example of a linear function.
True, because having a common difference also means it has a constant rate of change
False, because it's not shown on a graph
Show answer
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