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Formative Investigation: Sequences
By Theresa Joseph
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Last updated almost 2 years ago
7 questions
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CRITERION B
You will be assessed on the following strands
select and apply mathematical problem-solving techniques to discover complex patterns
describe patterns as relationships and/or general rules consistent with findings
verify and justify relationships and/or general rules
Formula Sheet
Linear Sequences: U
n
=an+b
1st Term = a+b
d = a
Quadratic Sequence: U
n
=an
2
+bn+c
1st Term = a+b+c
d
1
=3a+b
d
2
=2a
Observe the pattern on the right and create a 4th diagram to fit the pattern.
Question 1
1.
How many hollow and coloured tiles will be there in pattern 8?
Question 2
2.
Write a sequence denoting only the coloured tiles.
Question 3
3.
What is the general rule for the sequence of coloured tiles? Justify your answer.
Question 4
4.
Complete the following table by counting the total number of tiles in each pattern:
Question 5
5.
What kind of sequence is represented above? Justify using a difference diagram.
Question 6
6.
Find the general rule for the table you created. Verify your rule using a couple of terms from the sequence.
Question 7
7.
Using your general rule, predict how many tiles the 100th pattern will have.
Command terms:
Apply:
Use knowledge or understanding in a given situation.
Explain:
Give a detailed account including reasons or causes.
State:
Give a specific name, value or brief answer without explanation or calculation
Suggest:
Propose a solution, hypothesis or other possible explanation
Verify:
Provide evidence that validates the result
Justify:
Give valid reasons or evidence to support an answer or conclusion
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