9 Here are the first three patterns in a sequence.
(a) Draw Pattern 4 in the sequence.
Pattern 4
[1]
(b) Without drawing it, work out how many dots there are in Pattern 8. Explain how you decide. [2]
(c) Pattern \(n\) has 196 dots.
Find the value of \(n\). [1]
Mark scheme (a)
Answer
Marks
Part marks and guidance
1
Four rows of four dots roughly in a square pattern
Mark scheme (b)
Answer
Marks
Part marks and guidance
64 and 8 rows of 8 oe
2
B1 for 64 M1 for \(8 \times 8\) oe seen or The differences increase by 2 oe with at least 49 + 15 shown
Ignore any drawings oe = \(8^2\) or 8 + 8 + ....8 (eight times) or 1, 4, 9, 16, 25, 36, 49, 64 seen or the pattern number squared Do not accept Square numbers alone as a justification but accept It is the 8th square number for M1
