{"status": "success", "data": {"description_md": "**POTD April 9, 2024**\n\nThe sequence $\\{a_n\\}$ satisfies the property that $a_1=\\sin 17^\\circ{},$ and for $n \\geq 1, 12a_n-16a_{n+1}=16^n\\cdot a_n ^3$. Find the positive integer $k$ for which $a_k$ is the $17^\\text{th}$ smallest term in the list $a_1,a_2,\\ldots,a_{2015}.$", "description_html": "<p><strong>POTD April 9, 2024</strong></p>&#10;<p>The sequence <span class=\"katex--inline\">\\{a_n\\}</span> satisfies the property that <span class=\"katex--inline\">a_1=\\sin 17^\\circ{},</span> and for <span class=\"katex--inline\">n \\geq 1, 12a_n-16a_{n+1}=16^n\\cdot a_n ^3</span>. Find the positive integer <span class=\"katex--inline\">k</span> for which <span class=\"katex--inline\">a_k</span> is the <span class=\"katex--inline\">17^\\text{th}</span> smallest term in the list <span class=\"katex--inline\">a_1,a_2,\\ldots,a_{2015}.</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #122", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}