// Numbas version: exam_results_page_options
{"name": "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": {"description": "<p>Find the nth term of an Arithmetic progression</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "type": "question", "preamble": {"css": "", "js": ""}, "advice": "<p>If the difference between successive pairs of terms is a constant then the series under examination is an arithmetic progression.</p>\n<p>Ths first term is \\(a\\) and the common difference is \\(d\\).</p>\n<p>The formula for the nth term of the series is given by: &nbsp; &nbsp;\\(T_n=a+(n-1)d\\)</p>\n<p>In this example \\(a=\\var{a}\\), &nbsp;\\(d = \\var{d}\\) &nbsp;and &nbsp;\\(n = \\var{n}\\)</p>\n<p style=\"padding-left: 30px;\">\\(T_\\var{n}=\\var{a}+\\simplify{{n}-1}*\\var{d}\\)</p>\n<p style=\"padding-left: 30px;\">\\(T_\\var{n}=\\var{a}+\\simplify{({n}-1)*{d}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(T_\\var{n}=\\simplify{{a}+({n}-1)*{d}}\\)</p>", "rulesets": {}, "variable_groups": [], "name": "Arithmetic progression: The nth term of a series", "ungrouped_variables": ["a", "d", "n"], "functions": {}, "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(10..21#1)", "description": "", "templateType": "randrange"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..12#1)", "description": "", "templateType": "randrange"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(2..11#1)", "description": "", "templateType": "randrange"}}, "statement": "<p>The first three terms of a series are given by: &nbsp;</p>\n<p style=\"padding-left: 60px;\">\\(\\var{a} + \\simplify{{a}+{d}} + \\simplify{{a}+2*{d}}\\,+ \\, ...........\\)</p>", "parts": [{"showFeedbackIcon": true, "type": "gapfill", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": 0, "unitTests": [], "gaps": [{"type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "maxValue": "{a}+({n}-1)*{d}", "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "unitTests": [], "mustBeReducedPC": 0, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "extendBaseMarkingAlgorithm": true, "marks": "2", "minValue": "{a}+({n}-1)*{d}", "mustBeReduced": false, "showFeedbackIcon": false, "variableReplacements": [], "allowFractions": false}], "sortAnswers": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "prompt": "<p>Calculate the $\\var{n}$ (st/th) term of the series.</p>\n<p style=\"text-align: left; padding-left: 30px;\">\\(u_\\var{n}=\\)&nbsp;[[0]]</p>", "variableReplacements": []}], "contributors": [{"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Angharad Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/315/"}, {"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}