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{"name": "Computing terms in a recurrence relation 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "extensions": [], "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d", "f"], "parts": [{"gaps": [{"adaptiveMarkingPenalty": 0, "answer": "{a}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}, {"adaptiveMarkingPenalty": 0, "answer": "{b}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}, {"adaptiveMarkingPenalty": 0, "answer": "{a}+{b}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}, {"adaptiveMarkingPenalty": 0, "answer": "{a}+2{b}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}, {"adaptiveMarkingPenalty": 0, "answer": "2{a}+3{b}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}, {"adaptiveMarkingPenalty": 0, "answer": "3{a}+5{b}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}, {"adaptiveMarkingPenalty": 0, "answer": "5{a}+8{b}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}, {"adaptiveMarkingPenalty": 0, "answer": "8{a}+13{b}", "marks": 1, "type": "jme", "checkingType": "absdiff", "checkingAccuracy": 0.001, "checkVariableNames": false, "failureRate": 1, "useCustomName": false, "vsetRangePoints": 5, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "variableReplacements": [], "customName": "", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showPreview": true, "valuegenerators": []}], "showCorrectAnswer": true, "prompt": "<p>Compute the first eight terms of this recurrence relation.</p>\n<p>F(1) =&nbsp;[[0]]</p>\n<p>F(2) =&nbsp;[[1]]</p>\n<p>F(3) =&nbsp;[[2]]</p>\n<p>F(4) =&nbsp;[[3]]</p>\n<p>F(5) =&nbsp;[[4]]</p>\n<p>F(6) =&nbsp;[[5]]</p>\n<p>F(7) =&nbsp;[[6]]</p>\n<p>F(8) =&nbsp;[[7]]</p>", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "gapfill", "sortAnswers": false, "customName": "", "marks": 0, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "variableReplacements": [], "useCustomName": false}], "variables": {"d": {"description": "", "definition": "c-1", "group": "Ungrouped variables", "name": "d", "templateType": "anything"}, "f": {"description": "", "definition": "c-2", "group": "Ungrouped variables", "name": "f", "templateType": "anything"}, "c": {"description": "", "definition": "random(80..100)", "group": "Ungrouped variables", "name": "c", "templateType": "anything"}, "a": {"description": "", "definition": "random(1..5)", "group": "Ungrouped variables", "name": "a", "templateType": "anything"}, "b": {"description": "", "definition": "random(1..5 except a)", "group": "Ungrouped variables", "name": "b", "templateType": "anything"}}, "advice": "", "preamble": {"css": "", "js": ""}, "tags": [], "statement": "<p>Consider the following recurrence relation:</p>\n<p>\\[F(n)=\\begin{cases}\\var{a} &amp; if &amp; n=1\\\\ \\var{b} &amp; if &amp; n=2\\\\ F(n-1) + F(n-2) &amp; if &amp; n\\geq3 \\end{cases}\\]</p>\n<p></p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "name": "Computing terms in a recurrence relation 4", "metadata": {"licence": "None specified", "description": ""}, "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/"}]}