// Numbas version: exam_results_page_options
{"name": "Find a particular term of a sequence using the given formula", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Given a formula for a sequence, calculate a given term.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["n"], "type": "question", "rulesets": {}, "advice": "<h4></h4>\n<h4></h4>\n<p>Substitute $n = \\var{n}$ into the formula for the sequence.</p>\n<p>\\[\\]</p>\n<p>\\begin{align}<br/>a_n &amp;= \\frac{\\var{a}n(n+\\var{b})}{\\var{c}} \\\\[0.5em]<br/>a_{\\var{n}}&amp;= \\simplify[]{ ({a}*{n}*({n}+{b}))/{c} } \\\\[0.5em]<br/>&amp;=\\var{a*n*(n+b)/c}<br/>\\end{align}</p>\n<p></p>", "variables": {"b": {"description": "", "definition": "random(2..7)c", "group": "seq' eqn' question c)", "name": "b", "templateType": "anything"}, "c": {"description": "", "definition": "random(2..5)", "group": "seq' eqn' question c)", "name": "c", "templateType": "anything"}, "a": {"description": "", "definition": "random(2..5)", "group": "seq' eqn' question c)", "name": "a", "templateType": "anything"}, "n": {"description": "", "definition": "random(3..9 except 5)*c", "group": "Ungrouped variables", "name": "n", "templateType": "anything"}}, "statement": "", "name": "Find a particular term of a sequence using the given formula", "parts": [{"scripts": {}, "variableReplacements": [], "type": "gapfill", "prompt": "<p>Find the $\\var{n}^\\text{th}$ term of the sequence with formula:&nbsp;</p>\n<p>\\[a_n=\\frac{\\var{a}n(n+\\var{b})}{\\var{c}}\\]</p>\n<p>$a_{\\var{n}}=$ [[0]]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerFraction": false, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "allowFractions": false, "minValue": "a*n*(n+b)/c", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "a*n*(n+b)/c", "mustBeReduced": false, "marks": "1", "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}], "showFeedbackIcon": true, "marks": 0}], "tags": ["taxonomy"], "preamble": {"js": "", "css": ""}, "variable_groups": [{"name": "seq' eqn' question c)", "variables": ["a", "b", "c"]}], "functions": {}, "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}