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Here are the first three patterns in a sequence - OCR - GCSE Maths - Question 9 - 2019 - Paper 1
Question 9
Here are the first three patterns in a sequence. Pattern 1 • Pattern 2 • • • Pattern 3 • • • • (a) Draw Pattern 4 in the sequence. Pattern 4 (b) Without drawi... show full transcript
Worked Solution & Example Answer:Here are the first three patterns in a sequence - OCR - GCSE Maths - Question 9 - 2019 - Paper 1
Step 1
Step 2
Without drawing it, work out how many dots there are in Pattern 8. Explain how you decide.
Answer
There are 64 dots in Pattern 8.
To arrive at this conclusion, I observe the sequence of rows in each pattern. The number of dots is increasing systematically:
- Pattern 1 has 1 dot (1 row of 1 dot)
- Pattern 2 has 3 dots (1 row of 3 dots)
- Pattern 3 has 6 dots (2 rows of 3 dots)
The number of dots in each pattern seems to increment in squares:
- Each pattern can be represented as squares where Pattern n corresponds to the square of n. Thus, Pattern 8 has dots.
Therefore, I conclude that Pattern 8 contains 64 dots.