// Numbas version: exam_results_page_options {"name": "Simon's copy of Arithmetic progression: The sum of the first n terms of a series", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "
Find the sum of the first n terms of an arithmetic progression
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "The first three terms of a series are given by:
\n\\(\\var{a} + \\simplify{{a}+{d}} + \\simplify{{a}+2*{d}}\\,+ \\, ...........\\)
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\n\\(S_\\var{n}=\\) [[0]]
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\nThs first term is \\(a\\) and the common difference is \\(d\\).
\nThe formula for the nth term of the series is given by: \\(S_n=\\frac{n}{2}\\left(2a+(n-1)d\\right)\\)
\nIn this example \\(a=\\var{a}\\), \\(d = \\var{d}\\) and \\(n = \\var{n}\\)
\n\\(S_\\var{n}=\\frac{\\var{n}}{2}\\left(2\\times\\var{a}+(\\var{n}-1)\\var{d}\\right)\\)
\n\\(S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}}+\\simplify{({n}-1)*{d}}\\right)\\)
\n\\(S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}+({n}-1)*{d}}\\right)\\)
\n\\(S_\\var{n}=\\simplify{{n}*{a}+{n}*({n}-1)*{d}/2}\\)
\n", "preamble": {"css": "", "js": ""}, "extensions": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}