// Numbas version: exam_results_page_options
{"name": "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": [{"variable_groups": [], "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-NonCommercial 4.0 International", "description": "<p>Find the nth term of a Geometric progression</p>"}, "tags": [], "ungrouped_variables": ["a", "r", "n"], "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 1, "precisionMessage": "You have not given your answer to the correct precision.", "showPrecisionHint": true, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "strictPrecision": false, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "type": "numberentry", "precisionType": "dp", "showFeedbackIcon": true, "precision": "1", "minValue": "{a}*r^({n}-1)", "maxValue": "{a}*r^({n}-1)", "variableReplacements": [], "allowFractions": false}], "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>", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}}], "functions": {}, "preamble": {"css": "", "js": ""}, "variables": {"n": {"group": "Ungrouped variables", "description": "", "definition": "random(4..19#1)", "name": "n", "templateType": "randrange"}, "a": {"group": "Ungrouped variables", "description": "", "definition": "random(1..12#1)", "name": "a", "templateType": "randrange"}, "r": {"group": "Ungrouped variables", "description": "", "definition": "random(0.2..3#0.2)", "name": "r", "templateType": "randrange"}}, "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>", "type": "question", "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "extensions": [], "name": "Geometric progression: The nth term of a series", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}