2023 AMC 10B Problem 23

An arithmetic sequence of positive integers has n \ge 3 terms, initial term a, and common difference d \gt 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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.