// Numbas version: exam_results_page_options
{"name": "Geometric progression: The sum of the first n terms of a geometric progression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Find the sum of the first n terms of a Geometric progression</p>"}, "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 sum of the first \\(n\\)&nbsp;terms of the series is given by: &nbsp; &nbsp;\\(S_n=\\frac{a(1-r^{n})}{1-r}\\)</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;\">\\(S_\\var{n}=\\frac{\\var{a}(1-(\\var{r})^{\\var{n}})}{1-\\var{r}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(S_\\var{n}=\\frac{\\var{a}*(\\simplify{1-{r}^{n}})}{\\simplify{1-{r}}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(S_\\var{n}=\\frac{\\simplify{{a}*(1-{r}^{n})}}{\\simplify{1-{r}}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(S_\\var{n}=\\var{s}\\)</p>", "variable_groups": [], "parts": [{"showFeedbackIcon": true, "marks": 0, "scripts": {}, "variableReplacements": [], "prompt": "<p>Calculate the sum of the first \\(\\var{n}\\) terms of the series.</p>\n<p style=\"text-align: left; padding-left: 30px;\">\\(S_\\var{n}=\\)&nbsp;[[0]]</p>", "showCorrectAnswer": true, "type": "gapfill", "gaps": [{"precision": "1", "minValue": "{s}", "scripts": {}, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "showPrecisionHint": true, "allowFractions": false, "precisionPartialCredit": 0, "marks": 1, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "maxValue": "{s}", "correctAnswerFraction": false, "variableReplacements": [], "strictPrecision": false, "mustBeReduced": false, "type": "numberentry", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst"}], "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>", "preamble": {"js": "", "css": ""}, "rulesets": {}, "variables": {"n": {"definition": "random(4..19#1)", "templateType": "randrange", "name": "n", "group": "Ungrouped variables", "description": ""}, "a": {"definition": "random(1..12#1)", "templateType": "randrange", "name": "a", "group": "Ungrouped variables", "description": ""}, "s": {"definition": "({a}*(1-{r}^{n}))/(1-{r})", "templateType": "anything", "name": "s", "group": "Ungrouped variables", "description": ""}, "r": {"definition": "random(0.2..3#0.2)", "templateType": "randrange", "name": "r", "group": "Ungrouped variables", "description": ""}}, "extensions": [], "ungrouped_variables": ["a", "r", "n", "s"], "functions": {}, "name": "Geometric progression: The sum of the first n terms of a geometric progression", "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}