1. 4n n – n
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

2. 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?

3. 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?

4. Where would you place the numbers 1- 9?
Using Venn Diagrams 1 2 3 4 5 6 7 8 9
In the sequence 2n
In the sequence 3n
Where would you place the numbers 1- 9?

5. Where would you place this nth term?
Using Venn Diagrams
Common difference of +4
First term is 7
4n + 2
Where would you place this nth term?
4n + 2

6. 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?

7. 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?

8. A B D C 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!

9. 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!

10. 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!

11. 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!

12. 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!

13. 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?