// Numbas version: exam_results_page_options
{"name": "Geometric series 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"td": {"name": "td", "group": "Ungrouped variables", "definition": "random(3..5)", "description": "", "templateType": "anything"}, "tr": {"name": "tr", "group": "Ungrouped variables", "definition": "random(4..9)", "description": "", "templateType": "anything"}, "tsum": {"name": "tsum", "group": "Ungrouped variables", "definition": "random(11..19 except 21 except 22 except 23)", "description": "", "templateType": "anything"}, "t1": {"name": "t1", "group": "Ungrouped variables", "definition": "td*random(10..100)", "description": "", "templateType": "anything"}}, "advice": "<p>To find common ratio, simply divide one term by its predecessor.</p>\n<p>To find the $n$<sup>th&nbsp;</sup>term, multiply&nbsp;the first term a by the common ratio r to the power of n-1, ie ${a}{r^{n-1}}$</p>\n<p>Formula for the sum of the first $n$ terms is &nbsp;<img src=\"http://www.purplemath.com/modules/series/sum19.gif\" width=\"111\" height=\"49\" border=\"0\" alt=\"sum, from i = 1 to n, of a-sub-i  is equal to (a) [ (1 - r^n) / (1 - r) ]\"/>&nbsp;where $r$ is the common ratio and $a$ is the first term</p>\n<p>Formula for the infinite sum, providing $| r |&lt;1$, is&nbsp;<img src=\"http://www.purplemath.com/modules/series/sum20.gif\" width=\"88\" height=\"48\" border=\"0\" alt=\"sum, from i = 1 to infinity, of a-sub-i  is equal to  a/(1 - r)\"/>&nbsp;<span color=\"#FFFFFF\" face=\"Arial\" size=\"1\" style=\"color: #ffffff; font-family: Arial; font-size: xx-small;\">C</span></p>", "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "name": "Geometric series 2", "parts": [{"checkingType": "absdiff", "useCustomName": false, "answerSimplification": "all,fractionnumbers", "marks": 1, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "type": "jme", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "valuegenerators": [], "showPreview": true, "scripts": {}, "variableReplacements": [], "customName": "", "prompt": "<p>Find the $\\var{tr}$<sup>th&nbsp;</sup>term</p>", "unitTests": [], "answer": "(-1)^({tr}-1){t1}/(({td})^({tr}-1))", "variableReplacementStrategy": "originalfirst"}, {"checkingType": "absdiff", "useCustomName": false, "answerSimplification": "all,fractionnumbers", "marks": 1, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "type": "jme", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "valuegenerators": [{"name": "n", "value": ""}], "showPreview": true, "scripts": {}, "variableReplacements": [], "customName": "", "prompt": "<p>Find the $n$<sup>th</sup> term</p>", "unitTests": [], "answer": "(-1)^(n+1){t1}/(({td})^(n-1))", "variableReplacementStrategy": "originalfirst"}, {"checkingType": "absdiff", "useCustomName": false, "marks": 1, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "type": "jme", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "valuegenerators": [], "showPreview": true, "scripts": {}, "variableReplacements": [], "customName": "", "prompt": "<p>Find the sum of the first $\\var{tsum}$ terms</p>", "unitTests": [], "answer": "{t1}(1-(-1/{td})^{tsum})/(1+(1/{td}))", "variableReplacementStrategy": "originalfirst"}, {"checkingType": "absdiff", "useCustomName": false, "answerSimplification": "all,fractionnumbers", "marks": 1, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "type": "jme", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "valuegenerators": [], "showPreview": true, "scripts": {}, "variableReplacements": [], "customName": "", "prompt": "<p>Find the sum to infinity of the series&nbsp;</p>", "unitTests": [], "answer": "{t1}/(1-(-1/{td}))", "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "variable_groups": [], "statement": "<p>For the geometric series:</p>\n<p>$\\var{t1} - \\simplify{{t1}/{td}} + \\simplify{{t1}/{td}^2} - \\simplify{{t1}/{td}^3} +...$</p>\n<p></p>", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "ungrouped_variables": ["t1", "tr", "tsum", "td"], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}