Subjects algebra

Sequence Rule

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1. **Stating the problem:** Victoria creates a sequence of tiles and wants to find the rule that relates the entry number to the number of tiles used. 2. **Understanding the options:** - Option A: Number of tiles = entry number \( \times \) entry number, i.e., number of tiles = $n^2$. - Option B: Number of tiles = entry number + entry number, i.e., number of tiles = $2n$. - Option C: No rule is used. - Option D: Number of tiles = 1 for all entries. 3. **Analyzing the options:** - If the number of tiles grows as $n^2$, the sequence is quadratic. - If the number of tiles grows as $2n$, the sequence is linear with slope 2. - If the number of tiles is always 1, the sequence is constant. - If no rule is used, the sequence is random. 4. **Conclusion:** Since Victoria made a table showing the relationship, she must be using a rule. Without the actual table values, the most common simple rules are options A or B. 5. **Final answer:** Based on typical sequences, the most reasonable rule is option B: the number of tiles is equal to the entry number plus itself, i.e., number of tiles = $2n$. Therefore, Victoria uses rule B.