// Numbas version: exam_results_page_options {"name": "Simon's copy of Arithmetic progression: The nth term of a series", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "
Find the nth term of an Arithmetic progression
"}, "tags": [], "ungrouped_variables": ["a", "d", "n"], "variable_groups": [], "variables": {"d": {"definition": "random(2..11#1)", "name": "d", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}, "a": {"definition": "random(1..12#1)", "name": "a", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}, "n": {"definition": "random(4..19#1)", "name": "n", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}}, "name": "Simon's copy of Arithmetic progression: The nth term of a series", "parts": [{"showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "maxValue": "{a}+({n}-1)*{d}", "unitTests": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "minValue": "{a}+({n}-1)*{d}", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "mustBeReduced": false, "marks": 1, "mustBeReducedPC": 0, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "allowFractions": false, "type": "numberentry"}], "showFeedbackIcon": true, "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": "", "prompt": "Calculate the \\(\\var{n}th\\) term of the series.
\n\\(T_\\var{n}=\\) [[0]]
", "marks": 0, "sortAnswers": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "preamble": {"css": "", "js": ""}, "statement": "The first three terms of a series are given by:
\n\\(\\var{a} + \\simplify{{a}+{d}} + \\simplify{{a}+2*{d}}\\,+ \\, ...........\\)
", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "advice": "If the difference between successive pairs of terms is a constant then the series under examination is an arithmetic progression.
\nThs first term is \\(a\\) and the common difference is \\(d\\).
\nThe formula for the nth term of the series is given by: \\(T_n=a+(n-1)d\\)
\nIn this example \\(a=\\var{a}\\), \\(d = \\var{d}\\) and \\(n = \\var{n}\\)
\n\\(T_\\var{n}=\\var{a}+(\\var{n}-1)\\times\\var{d}\\)
\n\\(T_\\var{n}=\\var{a}+\\simplify{({n}-1)*{d}}\\)
\n\\(T_\\var{n}=\\simplify{{a}+({n}-1)*{d}}\\)
", "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/"}]}