// Numbas version: exam_results_page_options
{"name": "Arithmetic Sequences - Common Difference and Term", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Arithmetic Sequences - Common Difference and Term", "tags": [], "metadata": {"description": "Based on first and second term of an arithmetic sequence find common difference and eighth term.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>In an arithmetic sequence the first term is {a}&nbsp;and the second term is {b}.</p>", "advice": "<p>The common difference is the difference between any two consecutive terms. In this case the first and second term.&nbsp;</p>\n<p></p>\n<p>common difference = $\\var{b} - \\var{a} = \\var{d}$</p>\n<p></p>\n<p>To find any term in a sequence use the formula $u_n =&nbsp;u_1 + (n-1)d$</p>\n<p>In this case $u_8 = \\var{a} + 7 \\times \\var{d} = \\var{a + 7d}$</p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3 .. 7#1)", "description": "<p>first term</p>", "templateType": "randrange"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1 .. 5#1)", "description": "<p>common difference (restricted to small integers)</p>", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "a+d", "description": "<p>second term based on common difference.</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "d", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the common difference.</p>", "minValue": "{b}-{a}", "maxValue": "{b}-{a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the eighth term.</p>", "minValue": "7*{b}-6*{a}", "maxValue": "7*{b}-6*{a}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "eu", "plain-eu"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}]}], "contributors": [{"name": "Johnathan Gregg", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4974/"}]}