{"status": "success", "data": {"description_md": "Let $S_n$ be the sum of the first $n$ terms of an arithmetic sequence that has a common difference of $2$. The quotient $\\frac{S_{3n}}{S_n}$ does not depend on $n$. What is $S_{20}$?\n\n$\\textbf{(A) } 340 \\qquad \\textbf{(B) } 360 \\qquad \\textbf{(C) } 380 \\qquad \\textbf{(D) } 400 \\qquad \\textbf{(E) } 420$", "description_html": "<p>Let  <span class=\"katex--inline\">S_n</span>  be the sum of the first  <span class=\"katex--inline\">n</span>  terms of an arithmetic sequence that has a common difference of  <span class=\"katex--inline\">2</span> . The quotient  <span class=\"katex--inline\">\\frac{S_{3n}}{S_n}</span>  does not depend on  <span class=\"katex--inline\">n</span> . What is  <span class=\"katex--inline\">S_{20}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 340 \\qquad \\textbf{(B) } 360 \\qquad \\textbf{(C) } 380 \\qquad \\textbf{(D) } 400 \\qquad \\textbf{(E) } 420</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": 3, "problem_name": "2022 AMC 10B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10B_p16", "prev": "/problem/22_amc10B_p14"}}