{"status": "success", "data": {"description_md": "The figures $F_1$, $F_2$, $F_3$, and $F_4$ shown are the first in a sequence of figures. For $n\\ge3$, $F_n$ is constructed from $F_{n - 1}$ by surrounding it with a square and placing one more diamond on each side of the new square than $F_{n - 1}$ had on each side of its outside square. For example, figure $F_3$ has $13$ diamonds. How many diamonds are there in figure $F_{20}$?\n\n<center>\n<img class=\"problem-image\" height=\"115\" src=\"https://latex.artofproblemsolving.com/d/2/4/d24a6830ee3382e3945990d8af2e9e00ba14c85e.png\" width=\"355\"/>\n</center><br>\n\n$\\mathrm{(A)}\\ 401\n\\qquad\n\\mathrm{(B)}\\ 485\n\\qquad\n\\mathrm{(C)}\\ 585\n\\qquad\n\\mathrm{(D)}\\ 626\n\\qquad\n\\mathrm{(E)}\\ 761$", "description_html": "<p>The figures <span class=\"katex--inline\">F_1</span>, <span class=\"katex--inline\">F_2</span>, <span class=\"katex--inline\">F_3</span>, and <span class=\"katex--inline\">F_4</span> shown are the first in a sequence of figures. For <span class=\"katex--inline\">n\\ge3</span>, <span class=\"katex--inline\">F_n</span> is constructed from <span class=\"katex--inline\">F_{n - 1}</span> by surrounding it with a square and placing one more diamond on each side of the new square than <span class=\"katex--inline\">F_{n - 1}</span> had on each side of its outside square. For example, figure <span class=\"katex--inline\">F_3</span> has <span class=\"katex--inline\">13</span> diamonds. How many diamonds are there in figure <span class=\"katex--inline\">F_{20}</span>?</p>&#10;<center>&#10;<img class=\"problem-image\" height=\"115\" src=\"https://latex.artofproblemsolving.com/d/2/4/d24a6830ee3382e3945990d8af2e9e00ba14c85e.png\" width=\"355\"/>&#10;</center><br/>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 401&#10;\\qquad&#10;\\mathrm{(B)}\\ 485&#10;\\qquad&#10;\\mathrm{(C)}\\ 585&#10;\\qquad&#10;\\mathrm{(D)}\\ 626&#10;\\qquad&#10;\\mathrm{(E)}\\ 761</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 AMC 10A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc10A_p16", "prev": "/problem/09_amc10A_p14"}}