// 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": [{"functions": {}, "ungrouped_variables": ["t1", "tr", "tsum", "td"], "name": "Geometric series 2", "tags": [], "preamble": {"css": "", "js": ""}, "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>", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>Find the $\\var{tr}$<sup>th&nbsp;</sup>term</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "(-1)^({tr}-1){t1}/(({td})^({tr}-1))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>Find the $n$<sup>th</sup> term</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "(-1)^(n+1){t1}/(({td})^(n-1))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>Find the sum of the first $\\var{tsum}$ terms</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{t1}(1-(-1/{td})^{tsum})/(1+(1/{td}))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>Find the sum to infinity of the series&nbsp;</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,fractionnumbers", "scripts": {}, "answer": "{t1}/(1-(-1/{td}))", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"tsum": {"definition": "random(11..19 except 21 except 22 except 23)", "templateType": "anything", "group": "Ungrouped variables", "name": "tsum", "description": ""}, "td": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "td", "description": ""}, "tr": {"definition": "random(4..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "tr", "description": ""}, "t1": {"definition": "td*random(10..100)", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}