This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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2n + 1
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e) The pattern for the number of matches () based on the number of triangles () is given by the rule . Using this rule, the completed table is:
f) If the 'number of triangles' is the input () and the 'number of matches' is the output (), the rule is:
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This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.