{"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 <span class=\"katex--inline\">9</span>.  If <span class=\"katex--inline\">2</span> is added to the second term and <span class=\"katex--inline\">20</span> 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>&#10;<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>&#10;", "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"}}