\begin{tabular}{lllll}
& $\bullet \bullet \bullet$ & $\bullet \bullet \bullet$ & \
& $\bullet$ & $\bullet \bullet$ & $\bullet \bullet$ & \
$(1)$ & $(2)$ & $(3)$ & $(4)$ & $(5)$
\end{tabular}

Question

\begin{tabular}{lllll} 
& $\bullet \bullet \bullet$ & $\bullet \bullet \bullet$ & \
& $\bullet$ & $\bullet \bullet$ & $\bullet \bullet$ & \
$(1)$ & $(2)$ & $(3)$ & $(4)$ & $(5)$
\end{tabular}

Accepted Answer

∻Pattern Sequences∻ ‖ Pattern 1 ⋮ The pattern starts with a single black dot, which can be represented as a $1 imes 1$ grid containing 1 dot. ‖ ‖ Pattern 2 ⋮ The second pattern shows four black dots arranged in a $2 imes 2$ grid, containing $2^2 = 4$ dots. ‖ ‖ Pattern 3 ⋮ The third pattern has nine black dots arranged in a $3 imes 3$ grid, containing $3^2 = 9$ dots. ‖ ‖ Pattern 4 ⋮ The fourth pattern consists of sixteen black dots arranged in a $4 imes 4$ grid, containing $4^2 = 16$ dots. ‖ ‖ Pattern 5 ⋮ The fifth pattern is an empty square outline, suggesting the continuation of the pattern with a $5 imes 5$ grid. ‖ ∻Pattern Rule∻ ⚹ The number of dots in each pattern follows the square of the pattern number, i.e., $n^2$ dots for the $n$th pattern. ⚹ ∻Answer∻ ⚹ The fifth pattern should contain $5^2 = 25$ black dots arranged in a $5 imes 5$ 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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