{"status": "success", "data": {"description_md": "A sequence of three real numbers form an arithmetic progression with a first term of 9.  If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression.  What is the smallest possible value for the third term of the geometric progression?\n\n$\\mathrm{(A) \\ } 1 \\qquad \\mathrm{(B) \\ } 4 \\qquad \\mathrm{(C) \\ } 36 \\qquad \\mathrm{(D) \\ } 49 \\qquad \\mathrm{(E) \\ } 81$", "description_html": "<p>A sequence of three real numbers form an arithmetic progression with a first term of 9.  If 2 is added to the second term and 20 is added to the third term, the three resulting numbers form a geometric progression.  What is the smallest possible value for the third term of the geometric progression?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 1 \\qquad \\mathrm{(B) \\ } 4 \\qquad \\mathrm{(C) \\ } 36 \\qquad \\mathrm{(D) \\ } 49 \\qquad \\mathrm{(E) \\ } 81</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": "2004 AMC 10A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc10A_p19", "prev": "/problem/04_amc10A_p17"}}