{"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":"950f94fb-174a-5910-bcfa-e5c948858194","task_key":"intermediate~5falgebra--test--950f94fb-174a-5910-bcfa-e5c948858194","task_revision_id":"1","upstream_id":"","short_description":"The sequence $\\{a_n\\}$ is defined by $$","config":"intermediate_algebra","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The sequence $\\\\{a_n\\\\}$ is defined by $$\\na_0 = 1,a_1 = 1, \\\\text{ and } a_n = a_{n - 1} + \\\\frac {a_{n - 1}^2}{a_{n - 2}}\\\\text{ for }n\\\\ge2.\\n$$The sequence $\\\\{b_n\\\\}$ is defined by $$\\nb_0 = 1,b_1 = 3, \\\\text{ and } b_n = b_{n - 1} + \\\\frac {b_{n - 1}^2}{b_{n - 2}}\\\\text{ for }n\\\\ge2.$$Find $\\\\frac {b_{32}}{a_{32}}$.\",\"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":[]}