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{"name": "Andrew's copy of Geometric progression: The nth term of a series", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "statement": "<p>The first three terms of a series are given by: &nbsp;</p>\n<p style=\"padding-left: 60px;\">\\(\\var{a} + \\simplify{{a}*{r}} + \\simplify{{a}*{r}^2}\\,+ \\, ...........\\)</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find the nth term of a Geometric progression</p>"}, "rulesets": {}, "variables": {"a": {"name": "a", "definition": "random(1..12#1)", "templateType": "randrange", "group": "Ungrouped variables", "description": ""}, "n": {"name": "n", "definition": "random(4..19#1)", "templateType": "randrange", "group": "Ungrouped variables", "description": ""}, "r": {"name": "r", "definition": "random(0.2..3#0.2)", "templateType": "randrange", "group": "Ungrouped variables", "description": ""}}, "advice": "<p>If the ratio&nbsp;between successive pairs of terms is a constant then the series under examination is a geometric progression.</p>\n<p>Ths first term is \\(a\\) and the common ratio&nbsp;is \\(r\\).</p>\n<p>The formula for the nth term of the series is given by: &nbsp; &nbsp;\\(T_n=ar^{n-1}\\)</p>\n<p>In this example \\(a=\\var{a}\\), &nbsp; \\(r = \\frac{\\simplify{{a}*{r}}}{\\var{a}}=\\var{r}\\) &nbsp;and &nbsp;\\(n = \\var{n}\\)</p>\n<p style=\"padding-left: 30px;\">\\(T_\\var{n}=\\var{a}*\\var{r}^{\\simplify{{n}-1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(T_\\var{n}=\\var{a}*\\simplify{{r}^{{n}-1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(T_\\var{n}=\\simplify{{a}*{r}^{{n}-1}}\\)</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "ungrouped_variables": ["a", "r", "n"], "functions": {}, "name": "Andrew's copy of Geometric progression: The nth term of a series", "variable_groups": [], "tags": [], "parts": [{"marks": 0, "scripts": {}, "showCorrectAnswer": true, "prompt": "<p>Calculate the \\(\\var{n}th\\) term of the series.</p>\n<p style=\"text-align: left; padding-left: 30px;\">\\(T_\\var{n}=\\)&nbsp;[[0]]</p>", "type": "gapfill", "variableReplacements": [], "gaps": [{"minValue": "{a}*r^({n}-1)", "precisionPartialCredit": 0, "precisionType": "dp", "showCorrectAnswer": true, "maxValue": "{a}*r^({n}-1)", "strictPrecision": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "marks": 1, "showPrecisionHint": true, "scripts": {}, "type": "numberentry", "precisionMessage": "You have not given your answer to the correct precision.", "precision": "1", "correctAnswerFraction": false, "allowFractions": false}], "variableReplacementStrategy": "originalfirst"}], "type": "question", "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}]}], "contributors": [{"name": "Andrew Dunbar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/770/"}]}