// Numbas version: finer_feedback_settings
{"name": "Computing terms in a recurrence relation 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "None specified", "description": ""}, "variables": {"c": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(80..100)", "name": "c"}, "d": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "c-1", "name": "d"}, "b": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(1..5)", "name": "b"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "random(2..9)", "name": "a"}, "f": {"group": "Ungrouped variables", "templateType": "anything", "description": "", "definition": "c-2", "name": "f"}}, "parts": [{"showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "prompt": "<p>Compute the first four terms of this recurrence relation.</p>\n<p>C(1) =&nbsp;[[0]]</p>\n<p>C(2) =&nbsp;[[1]]</p>\n<p>C(3) =&nbsp;[[2]]</p>\n<p>C(4) =&nbsp;[[3]]</p>", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"vsetRangePoints": 5, "checkVariableNames": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "type": "jme", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "answer": "{b}", "marks": 1, "customMarkingAlgorithm": ""}, {"vsetRangePoints": 5, "checkVariableNames": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "type": "jme", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "answer": "{b}+{a}", "marks": 1, "customMarkingAlgorithm": ""}, {"vsetRangePoints": 5, "checkVariableNames": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "type": "jme", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "answer": "{b}+2{a}", "marks": 1, "customMarkingAlgorithm": ""}, {"vsetRangePoints": 5, "checkVariableNames": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "type": "jme", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "answer": "{b}+3{a}", "marks": 1, "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "customMarkingAlgorithm": ""}, {"showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "prompt": "<p>Write $C(\\var{c})$ in terms of $C(\\var{d})$</p>\n<p>$C(\\var{c}) = C(\\var{d}) + $[[0]]</p>", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"vsetRangePoints": 5, "checkVariableNames": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "type": "jme", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "answer": "{a}", "marks": 1, "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "customMarkingAlgorithm": ""}, {"showCorrectAnswer": true, "unitTests": [], "type": "gapfill", "prompt": "<p>Write $C(\\var{c})$ in terms of $C(\\var{f})$</p>\n<p>$C(\\var{c}) = C(\\var{f}) + $[[0]]</p>", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "gaps": [{"vsetRangePoints": 5, "checkVariableNames": false, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "expectedVariableNames": [], "checkingType": "absdiff", "scripts": {}, "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "type": "jme", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "answer": "2*{a}", "marks": 1, "customMarkingAlgorithm": ""}], "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "customMarkingAlgorithm": ""}], "name": "Computing terms in a recurrence relation 1", "rulesets": {}, "tags": [], "advice": "", "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d", "f"], "functions": {}, "statement": "<p>Consider the following recurrence relation:</p>\n<p>\\[C(n)=\\begin{cases}\\var{b} &amp; if &amp; n=1\\\\ C(n-1) + \\var{a} &amp; if &amp; n\\geq2 \\end{cases}\\]</p>\n<p></p>", "type": "question", "contributors": [{"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}]}], "contributors": [{"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}