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Question
Math
Posted 3 months ago

\begin{tabular}{lllll} 
& \bullet \bullet \bullet & \bullet \bullet \bullet & \\
& \bullet & \bullet \bullet & \bullet \bullet & \\
(1)(1) & (2)(2) & (3)(3) & (4)(4) & (5)(5)
\end{tabular}
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Answer from Sia
Posted 3 months ago
Pattern Sequences
Pattern 1
The pattern starts with a single black dot, which can be represented as a 1×11 \times 1 grid containing 1 dot
Pattern 2
The second pattern shows four black dots arranged in a 2×22 \times 2 grid, containing 22=42^2 = 4 dots
Pattern 3
The third pattern has nine black dots arranged in a 3×33 \times 3 grid, containing 32=93^2 = 9 dots
Pattern 4
The fourth pattern consists of sixteen black dots arranged in a 4×44 \times 4 grid, containing 42=164^2 = 16 dots
Pattern 5
The fifth pattern is an empty square outline, suggesting the continuation of the pattern with a 5×55 \times 5 grid
Pattern Rule
The number of dots in each pattern follows the square of the pattern number, i.e., n2n^2 dots for the nnth pattern.
Answer
The fifth pattern should contain 52=255^2 = 25 black dots arranged in a 5×55 \times 5 grid.
Key Concept
Square Numbers
Explanation
Each pattern represents a square number, which is the product of an integer with itself.

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