// 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": [{"tags": ["taxonomy"], "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "maxValue": "a*n*(n+b)/c", "showFeedbackIcon": true, "minValue": "a*n*(n+b)/c", "variableReplacements": [], "allowFractions": false}], "prompt": "

Find the $\\var{n}^\\text{th}$ term of the sequence with formula:

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\$a_n=\\frac{\\var{a}n(n+\\var{b})}{\\var{c}}\$

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$a_{\\var{n}}=$ [[0]]

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Given a formula for a sequence, calculate a given term.

"}, "type": "question", "variables": {"c": {"group": "seq' eqn' question c)", "description": "", "definition": "random(2..5)", "name": "c", "templateType": "anything"}, "b": {"group": "seq' eqn' question c)", "description": "", "definition": "random(2..7)c", "name": "b", "templateType": "anything"}, "a": {"group": "seq' eqn' question c)", "description": "", "definition": "random(2..5)", "name": "a", "templateType": "anything"}, "n": {"group": "Ungrouped variables", "description": "", "definition": "random(3..9 except 5)*c", "name": "n", "templateType": "anything"}}, "advice": "\n\n

Substitute $n = \\var{n}$ into the formula for the sequence.

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\$\$

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\\begin{align}
a_n &= \\frac{\\var{a}n(n+\\var{b})}{\\var{c}} \\\\[0.5em]
a_{\\var{n}}&= \\simplify[]{ ({a}*{n}*({n}+{b}))/{c} } \\\\[0.5em]
&=\\var{a*n*(n+b)/c}
\\end{align}

\n

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