{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"2f0ff523-c3c2-5c66-92d8-45efb64f094b","task_key":"intermediate~5falgebra--test--2f0ff523-c3c2-5c66-92d8-45efb64f094b","task_revision_id":"1","upstream_id":"","short_description":"The Fibonacci numbers are defined recursively by the equation","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The Fibonacci numbers are defined recursively by the equation\\n\\\\[ F_n = F_{n - 1} + F_{n - 2}\\\\]for every integer $ n \\\\ge 2$, with initial values $ F_0 = 0$ and $ F_1 = 1$.  Let $ G_n = F_{3n}$ be every third Fibonacci number.  There are constants $ a$ and $ b$ such that every integer $ n \\\\ge 2$ satisfies\\n\\\\[ G_n = a G_{n - 1} + b G_{n - 2}.\\\\]Find $(a,b)$.\",\"type\":\"Intermediate Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}