// 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": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Find the nth term of an Arithmetic progression</p>"}, "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": {}, "extensions": [], "functions": {}, "ungrouped_variables": ["a", "d", "n"], "name": "Arithmetic progression: The nth term of a series", "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "variables": {"n": {"name": "n", "definition": "random(4..19#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}, "a": {"name": "a", "definition": "random(1..12#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange"}, "d": {"name": "d", "definition": "random(2..11#1)", "group": "Ungrouped variables", "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": [{"type": "gapfill", "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "gaps": [{"precision": "1", "maxValue": "{a}+({n}-1)*{d}", "showPrecisionHint": true, "allowFractions": false, "type": "numberentry", "strictPrecision": false, "marks": 1, "precisionPartialCredit": 0, "precisionType": "dp", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "mustBeReduced": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "minValue": "{a}+({n}-1)*{d}", "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "correctAnswerFraction": false}], "prompt": "<p>Calculate the \\(\\var{n}th\\) term of the series.</p>\n<p style=\"text-align: left; padding-left: 30px;\">\\(T_\\var{n}=\\)&nbsp;[[0]]</p>", "variableReplacements": []}], "contributors": [{"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": "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/"}]}