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Sample Question 23:
An arithmetic sequence of positive integers has \(n\ge3\) terms, initial term \(a\), and common difference \(d>1\). Carl wrote down all the terms in this sequence correctly except for one term, which was off by \(1\). The sum of the terms he wrote down was \(222\). What is \(a+d+n\)?
\(\textbf{(A) } 24 \qquad \textbf{(B) } 20 \qquad \textbf{(C) } 22 \qquad \textbf{(D) } 28 \qquad \textbf{(E) } 26\)