Sequences and Patterns in Mathematics
4n + 1 4n – 2
4n
•
What is the
common difference
in all three of the
sequences?
•
On your whiteboard, can you show me an
expression that would also give me a
common
difference
of 4?
•
And another
4n + 1 4n – 2
4n
•
Write down an nth term would give the multiples of
3.
•
Can you show me a different nth term that would
give another sequence with an common difference
of 3?
•
Can you show me an expression that would give
me a decreasing sequence with a common
difference of 5?
4n + 1 4n – 2
4n
•
Do any of the sequences above contain a term of
20?
•
Which sequence definitely does not contain the
term 536? How do you know?
•
None of the three sequences have any of the same
terms. Why is that?
Using Venn Diagrams
In the
sequence 3n
In the
sequence 2n
1
2
3
4
5
6
7
8
9
Where would you place
the numbers 1- 9?
Using Venn Diagrams
First term is 7
Common
difference of +4
Where would you
place this nth term?
4n + 2
4n + 2
Using Venn Diagrams
Can you write an
nth term that
would fit in this
region?
First term is 7
Common
difference of +4
4n + 2
Using Venn Diagrams
Can you write an
nth term that
would fit in this
region?
First term is 7
Common
difference of +4
4n + 2
D
Think of an nth term rule that could belong in each region
Sequence
contains the
number 20
Sequences is
increasing
A
B
C
D
If you think a region is impossible
to fill, convince me why!
D
Think of an nth term rule that could belong in each region
4
th
term = 10
Common
difference of
+3
A
B
C
D
If you think a region is impossible
to fill, convince me why!
D
Think of an nth term rule that could belong in each region
3
rd
term = 8
Common
difference of -5
A
B
C
D
If you think a region is impossible
to fill, convince me why!
H
Sequence is
increasing
1
st
term is 10
Sequence
contains the
number 24
A
B
C
D
E
F
G
Think of an nth term rule that could belong in each region
If you think a region is impossible
to fill, convince me why!
H
Common difference
between each term is
+ or - 6
Sequence
contains the
number 12
Sequence
contains exactly
3 negative terms
A
B
C
D
E
F
G
Think of an nth term rule that could belong in each region
If you think a region is impossible
to fill, convince me why!
Venn Diagrams Challenges
•
Which was the easiest region to complete, and which was the hardest?
•
Which region has the most possible examples, and which has the fewest?
•
If you think it is impossible to find an example for a particular region, convince
me why
•
What would you change a circle label to, to make the task easier/harder
•
Create your own Venn Diagram on this topic where it is possible to fill in all the
regions
•
Create your own Venn Diagram on this topic when it is impossible to fill in just 1
of the regions. How about one where it is impossible to fill in 2, 3, 4, etc
regions?
Dive into the world of sequences and patterns by exploring expressions, common differences, and nth terms. Discover how to create sequences with specific common differences, identify terms within sequences, and use Venn diagrams to visualize different scenarios. Uncover the rules for constructing nth terms in increasing and decreasing sequences with various common differences.
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Presentation Transcript
4n + 1 4n 2 4n What is the common difference in all three of the sequences? On your whiteboard, can you show me an expression that would also give me a common difference of 4? And another
4n + 1 4n 2 4n Write down an nth term would give the multiples of 3. Can you show me a different nth term that would give another sequence with an common difference of 3? Can you show me an expression that would give me a decreasing sequence with a common difference of 5?
4n + 1 4n 2 4n Do any of the sequences above contain a term of 20? Which sequence definitely does not contain the term 536? How do you know? None of the three sequences have any of the same terms. Why is that?
Using Venn Diagrams 1 2 3 4 5 6 7 8 9 In the In the sequence 3n sequence 2n Where would you place the numbers 1- 9?
Using Venn Diagrams Common difference of +4 First term is 7 4n + 2 Where would you place this nth term? 4n + 2
Using Venn Diagrams Common difference of +4 First term is 7 4n + 2 Can you write an nth term that would fit in this region?
Using Venn Diagrams Common difference of +4 First term is 7 4n + 2 Can you write an nth term that would fit in this region?
Think of an nth term rule that could belong in each region Sequences is increasing Sequence contains the number 20 A B D C D If you think a region is impossible to fill, convince me why!
Think of an nth term rule that could belong in each region Common difference of +3 4th term = 10 A B D C D If you think a region is impossible to fill, convince me why!
Think of an nth term rule that could belong in each region Common difference of -5 3rd term = 8 A B D C D If you think a region is impossible to fill, convince me why!
Think of an nth term rule that could belong in each region Sequence is increasing 1st term is 10 D B A G E F H C Sequence contains the number 24 If you think a region is impossible to fill, convince me why!
Think of an nth term rule that could belong in each region Sequence contains the number 12 Common difference between each term is + or - 6 D B A G E F H C Sequence contains exactly 3 negative terms If you think a region is impossible to fill, convince me why!
Venn Diagrams Challenges Which was the easiest region to complete, and which was the hardest? Which region has the most possible examples, and which has the fewest? If you think it is impossible to find an example for a particular region, convince me why What would you change a circle label to, to make the task easier/harder Create your own Venn Diagram on this topic where it is possible to fill in all the regions Create your own Venn Diagram on this topic when it is impossible to fill in just 1 of the regions. How about one where it is impossible to fill in 2, 3, 4, etc regions?
