{"status": "success", "data": {"description_md": "A sequence of three real numbers forms 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 in the geometric progression?\n\n$\\text {(A) } 1 \\qquad \\text {(B) } 4 \\qquad \\text {(C) } 36 \\qquad \\text {(D) } 49 \\qquad \\text {(E) }81$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A sequence of three real numbers forms 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 in the geometric progression?</p>&#10;<p> <span class=\"katex--inline\">\\text {(A) } 1 \\qquad \\text {(B) } 4 \\qquad \\text {(C) } 36 \\qquad \\text {(D) } 49 \\qquad \\text {(E) }81</span> </p>&#10;<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 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12A_p15", "prev": "/problem/04_amc12A_p13"}}