// Numbas version: exam_results_page_options
{"name": "Geometric series 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "ungrouped_variables": ["t1", "tr", "tsum", "r"], "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>", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"prompt": "<p>Find the $\\var{tr}$<sup>th&nbsp;</sup>term</p>", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "type": "numberentry", "showFeedbackIcon": true, "useCustomName": false, "minValue": "{t1}*(({r})^{{tr}-1})", "showCorrectAnswer": true, "marks": 1, "showFractionHint": true, "mustBeReducedPC": 0, "maxValue": "{t1}*(({r})^{{tr}-1})", "customName": "", "correctAnswerFraction": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "allowFractions": true, "variableReplacements": [], "unitTests": [], "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "mustBeReduced": false}, {"prompt": "<p>Find the $n$<sup>th</sup> term</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "n"}], "customName": "", "answer": "{t1}*(({r})^(n-1))", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all,fractionnumbers"}, {"prompt": "<p>Find the sum of the first $\\var{tsum}$ terms</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": 1, "checkVariableNames": false, "valuegenerators": [], "customName": "", "answer": "{t1}(1-({r})^{tsum})/((1-{r}))", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1}], "tags": [], "statement": "<p>For the geometric series:</p>\n<p>$\\var{t1}$<span data-jme-visible=\"{r}&gt;0\">+</span>$\\simplify{{t1}*{r}}$+$\\simplify{{t1}*{{r}^2}}$<span data-jme-visible=\"{r}&gt;0\">+</span>$\\simplify{{t1}*{{r}^3}}$+...</p>\n<p></p>", "variables": {"t1": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "tr", "name": "t1"}, "tsum": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(4..10)", "name": "tsum"}, "tr": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(4..10)", "name": "tr"}, "r": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(-4..4 except [1,0,-1])", "name": "r"}}, "rulesets": {}, "functions": {}, "extensions": [], "name": "Geometric series 1", "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/"}]}