math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
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1{2 "source_file": "./raw_volume-zh/volume6/chapter1-6.tex",3 "problem_type": "calculation",4 "problem": "例1. 设数列 $\\left\\{a_n\\right\\}$ 是一个三阶等差数列, 其前面的若干项为 $1,2,8,22$, $47,86, \\cdots$. 求 $\\left\\{a_n\\right\\}$ 的通项公式.",5 "solution": "解法二由定理 2 的结论,可设 $a_n=A n^3+B n^2+C n+D$, 其中 $A 、 B 、 C 、 D$ 待定.\n利用初始条件, 知\n$$\n\\left\\{\\begin{array}{l}\nA+B+C+D=1, \\\\\n8 A+4 B+2 C+D=2, \\\\\n27 A+9 B+3 C+D=8, \\\\\n64 A+16 B+4 C+D=22 .\n\\end{array}\\right.\n$$\n解得 $A=\\frac{1}{2}, B=-\\frac{1}{2}, C=-1, D=2$.\n所以 $a_n=\\frac{1}{2} n^3-\\frac{1}{2} n^2-n+2$.\n说明利用待定系数的方法求解高阶等差数列的通项公式也经常用到.",6 "remark": "",7 "figures": []8}