{"status": "success", "data": {"description_md": "The sequence $S_1, S_2, S_3, \\cdots, S_{10}$ has the property that every term beginning with the third is the sum of the previous two.  That is, $$S_n = S_{n-2} + S_{n-1} \\text{ for } n \\ge 3.$$ Suppose that $S_9 = 110$ and $S_7 = 42$.  What is $S_4$?\n\n$\\textbf{(A)}\\ 4\\qquad\\textbf{(B)}\\ 6\\qquad\\textbf{(C)}\\ 10\\qquad\\textbf{(D)}\\ 12\\qquad\\textbf{(E)}\\ 16\\qquad$\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>The sequence  <span class=\"katex--inline\">S_1, S_2, S_3, \\cdots, S_{10}</span>  has the property that every term beginning with the third is the sum of the previous two.  That is,  <span class=\"katex--display\">S_n = S_{n-2} + S_{n-1} \\text{ for } n \\ge 3.</span>  Suppose that  <span class=\"katex--inline\">S_9 = 110</span>  and  <span class=\"katex--inline\">S_7 = 42</span> .  What is  <span class=\"katex--inline\">S_4</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 4\\qquad\\textbf{(B)}\\ 6\\qquad\\textbf{(C)}\\ 10\\qquad\\textbf{(D)}\\ 12\\qquad\\textbf{(E)}\\ 16\\qquad</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": 2, "problem_name": "2013 AMC 12A Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p08", "prev": "/problem/13_amc12A_p06"}}