Arithmetic Sequences
Presentation
•
Mathematics
•
10th - 12th Grade
•
Medium
Standards-aligned
Abbie Gutzmer
Used 8+ times
FREE Resource
6 Slides • 12 Questions
1
LT 8: I can identify and use the formulas for arithmetic and geometric sequences.
GOAL: To further understand the arithmetic sequence; both in using and writing the sequence.
2
Fill in the Blanks
Type answer...
3
Fill in the Blanks
Type answer...
4
Multiple Choice
What is the difference between f(n) and an?
f(n) is a function (can be graphed) and an represents a sequence.
Nothing, they are interchangeable.
I need to find a few more values to determine the difference.
We can find infinitely many values using an and only five or six for f(n).
5
Multiple Choice
Given f(n) = 3n - 7 is a sequence that can be defined as an = 3n - 7;
f(10) = 23 and
f(10 - 1) = f(9) = 20,
which of the following statements is true?
f(9) is the an-1 for f(10)
20 is the an-1 for 23
23 is the an-1 for 20
Why an?
6
An Arithmetic Sequence
The value of each term is the value of the PREVIOUS term with a constant added. (or subtracted)
When we talk about terms we mean the VALUE at the term number.
Notation;
Term: an
Previous term: an-1
7
Consider f(n) = 3n - 7 again.
1st term is the value of f(1)
2nd term is the value of f(2)
3rd term is the value of f(3)
4th term is the value of f(4)
SEQUENCE IS THEN:
{-4, -1, 2, 5, ...}
YOU DON'T EVEN NEED THE FORMULA ANYMORE...
So...
8
The recursive definition of an arithmetic sequence.
First - define what is getting added or subtracted to the previous term.
3, 6, 9, 12, ...
We are adding 3 to the previous term.
THIS IS WHAT WE CALL THE COMMON DIFFERENCE ("d")
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Multiple Choice
Given the sequence;
1, 5, 9, 13, ...
which of the following is the recursive definition?
an=a(n−1)+4
an=a(n−1)+4; a1=1
an=n+4; a1=1
an=1+4n; a1=1
10
Multiple Choice
Given the sequence;
6, 17, 28, 39, 50....
write the recursive definition.
a1=6
a1=6
a1=6
a1=6
11
The explicit formula of an arithmetic sequence - YOU MAY WANT TO WRITE IT DOWN!
Use the common difference, plug into the formula and simplify.
3, 6, 9, 12, ...
Common difference is still 3
an = 3 + (n - 1)(3)
an = 3 + 3n - 3
an = 3n (THE EXPLICIT FORMULA)
Now you can find any term value!
All found by simplifying
12
Multiple Choice
13
Multiple Choice
Find the common difference: -34, -29, -24, -19, ...
Now, which of the following is the explicit formula of the sequence?
an = 5 + (n-1)(-34)
an = -34 + (n-1)(5)
an = -34(n) + (n-1)(5)
an = (n-1) + (-34)(5)
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Multiple Choice
Given the sequence: 25, 21, 17, 13,... Write the explicit formula. Then, SIMPLIFY your equation.
15
Multiple Choice
Given the sequence:
2, 8, 14, ...
Write the explicit formula.
(Hint: Write your formula and then simplify it.)
an= 2 + 6n
an= -6 + 6n
an= 6n - 4
an= 4 - 6n
16
Multiple Choice
Let's use it...Given a1 = 5 and d = 0.5, write the explicit formula and use it to find the 25th term
17
Multiple Choice
18
To Summarize
An arithmetic sequence is simply follows a linear pattern.
You need two parts to find the explicit formula of an arithmetic sequence; the first term and the common difference.
When one asks you to find the nth term of a sequence - you are looking for the EXPLICIT FORMULA.
You can use the EXPLICIT FORMULA to find ANY term in the sequence!!!
LT 8: I can identify and use the formulas for arithmetic and geometric sequences.
GOAL: To further understand the arithmetic sequence; both in using and writing the sequence.
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