{"status": "success", "data": {"description_md": "Consider the sequence of numbers: $4,7,1,8,9,7,6,\\ldots$ For $n>2$, the $n$-th term of the sequence is the units digit of the sum of the two previous terms. Let $S_n$ denote the sum of the first $n$ terms of this sequence. The smallest value of $n$ for which $S_n>10,000$ is: \n\n$\\text{(A) }1992<br>\\qquad<br>\\text{(B) }1999<br>\\qquad<br>\\text{(C) }2001<br>\\qquad<br>\\text{(D) }2002<br>\\qquad<br>\\text{(E) }2004$\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>Consider the sequence of numbers:  <span class=\"katex--inline\">4,7,1,8,9,7,6,\\ldots</span>  For  <span class=\"katex--inline\">n&gt;2</span> , the  <span class=\"katex--inline\">n</span> -th term of the sequence is the units digit of the sum of the two previous terms. Let  <span class=\"katex--inline\">S_n</span>  denote the sum of the first  <span class=\"katex--inline\">n</span>  terms of this sequence. The smallest value of  <span class=\"katex--inline\">n</span>  for which  <span class=\"katex--inline\">S_n&gt;10,000</span>  is:</p>&#10;<p> <span class=\"katex--inline\">\\text{(A) }1992\\qquad\\text{(B) }1999\\qquad\\text{(C) }2001\\qquad\\text{(D) }2002\\qquad\\text{(E) }2004</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": 5, "problem_name": "2002 AMC 12A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12A_p22", "prev": "/problem/02_amc12A_p20"}}