For the pattern \(1,~4,~7,~10,~13,~...\), test every rule below and report the complete set of matching labels.
A. Start at \(1\) and add \(3\) each time.
B. Multiply by \(3\) each time.
C. The \(n\)th term is \(3n~-~2\).
D. The \(n\)th term is \(n~+~3\).
E. The \(n\)th term is \(1~+~3(n~-~1)\).
What this problem is really about
Because several differently written rules can generate the same pattern, test every one rather than stopping after the first match. Recursive descriptions should reproduce each step from the starting term, while nth-term formulas should be evaluated at several positions and simplified when useful. This catches accidental one-term matches and reveals formulas that look different but are algebraically equivalent.