{"status": "success", "data": {"description_md": "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 $a+d+n$?\n\n$\\textbf{(A) } 24 \\qquad \\textbf{(B) } 20 \\qquad \\textbf{(C) } 22 \\qquad \\textbf{(D) } 28 \\qquad \\textbf{(E) } 26$", "description_html": "<p>An arithmetic sequence of positive integers has  <span class=\"katex--inline\">n\\ge3</span>  terms, initial term  <span class=\"katex--inline\">a</span> , and common difference  <span class=\"katex--inline\">d&gt;1</span> . Carl wrote down all the terms in this sequence correctly except for one term, which was off by  <span class=\"katex--inline\">1</span> . The sum of the terms he wrote down was  <span class=\"katex--inline\">222</span> . What is  <span class=\"katex--inline\">a+d+n</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 24 \\qquad \\textbf{(B) } 20 \\qquad \\textbf{(C) } 22 \\qquad \\textbf{(D) } 28 \\qquad \\textbf{(E) } 26</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2023 AMC 10B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10B_p24", "prev": "/problem/23_amc10B_p22"}}