// Numbas version: exam_results_page_options
{"name": "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": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Find the sum of the first n terms of an arithmetic progression</p>"}, "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;\\(S_n=\\frac{n}{2}\\left(2a+(n-1)d\\right)\\)</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;\">\\(S_\\var{n}=\\frac{\\var{n}}{2}\\left(2*\\var{a}+(\\var{n}-1)\\var{d}\\right)\\)</p>\n<p style=\"padding-left: 30px;\">\\(S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}}+\\simplify{({n}-1)*{d}}\\right)\\)</p>\n<p style=\"padding-left: 30px;\">\\(S_\\var{n}=\\simplify{{n}/{2}}\\left(\\simplify{2{a}+({n}-1)*{d}}\\right)\\)</p>\n<p style=\"padding-left: 30px;\">\\(S_\\var{n}=\\simplify{{n}*{a}+{n}*({n}-1)*{d}/2}\\)</p>\n<p style=\"padding-left: 30px;\"></p>", "tags": [], "functions": {}, "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>", "preamble": {"js": "", "css": ""}, "rulesets": {}, "variables": {"n": {"definition": "random(4..19#1)", "templateType": "randrange", "name": "n", "group": "Ungrouped variables", "description": ""}, "a": {"definition": "random(1..12#1)", "templateType": "randrange", "name": "a", "group": "Ungrouped variables", "description": ""}, "d": {"definition": "random(2..11#1)", "templateType": "randrange", "name": "d", "group": "Ungrouped variables", "description": ""}}, "extensions": [], "ungrouped_variables": ["a", "d", "n"], "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Arithmetic progression: The sum of the first n terms of a series", "parts": [{"scripts": {}, "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "prompt": "<p>Calculate the sum of the first \\(\\var{n}\\) terms of this series.</p>\n<p style=\"text-align: left; padding-left: 30px;\">\\(S_\\var{n}=\\)&nbsp;[[0]]</p>", "type": "gapfill", "marks": 0, "gaps": [{"minValue": "{n}*{a}+({n}-1)*{n}*{d}/2", "precision": "1", "scripts": {}, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "showPrecisionHint": true, "allowFractions": false, "precisionPartialCredit": 0, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "maxValue": "{n}*{a}+({n}-1)*{n}*{d}/2", "correctAnswerFraction": false, "variableReplacements": [], "strictPrecision": false, "mustBeReduced": false, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "mustBeReducedPC": 0}], "variableReplacementStrategy": "originalfirst"}], "variable_groups": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}