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Formative Investigation: Sequences

Last updated over 1 year ago
7 questions
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: Un=an+b
1st Term = a+b
d = a

Quadratic Sequence: Un=an2+bn+c
1st Term = a+b+c
d1=3a+b
d2=2a
Observe the pattern on the right and create a 4th diagram to fit the pattern.
1

How many hollow and coloured tiles will be there in pattern 8?

1

Write a sequence denoting only the coloured tiles.

1

What is the general rule for the sequence of coloured tiles? Justify your answer.

1

Complete the following table by counting the total number of tiles in each pattern:

1

What kind of sequence is represented above? Justify using a difference diagram.

1

Find the general rule for the table you created. Verify your rule using a couple of terms from the sequence.

1

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