// Numbas version: exam_results_page_options
{"name": "Geometric progression: The sum to infinity", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>The first three terms of a geometric progression are given by: &nbsp;</p>\n<p style=\"padding-left: 60px;\">\\(\\var{a} + \\simplify{{a}*{r}} + \\simplify{{a}*{r}^2}\\,+ \\, ...........\\)</p>", "metadata": {"description": "<p>Find the sum of the first n terms of a Geometric progression</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "preamble": {"js": "", "css": ""}, "functions": {}, "extensions": [], "variablesTest": {"maxRuns": 100, "condition": "r<>1"}, "name": "Geometric progression: The sum to infinity", "variable_groups": [], "rulesets": {}, "parts": [{"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "variableReplacements": [], "showFeedbackIcon": true, "sortAnswers": false, "marks": 0, "unitTests": [], "gaps": [{"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "precisionPartialCredit": 0, "unitTests": [], "correctAnswerStyle": "plain", "allowFractions": false, "showPrecisionHint": true, "marks": 1, "showFeedbackIcon": true, "precision": "3", "type": "numberentry", "variableReplacements": [], "minValue": "{s}", "precisionType": "dp", "showCorrectAnswer": true, "strictPrecision": false, "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{s}", "scripts": {}, "mustBeReducedPC": 0, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "scripts": {}, "prompt": "<p>Calculate the sum&nbsp;to infinity of the series.</p>\n<p style=\"text-align: left; padding-left: 30px;\">\\(S_\\infty=\\)&nbsp;[[0]]</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>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>Since $ |r| = \\var{r} &lt; 1 $ then the sum to infinity exists and can be calculated as:</p>\n<p>\\(S_\\infty=\\frac{a}{1-r}\\)</p>\n<p>So for our example:</p>\n<p>\\(S_\\infty=\\frac{\\var{a}}{1-\\var{r}}\\)</p>\n<p>\\(S_\\var{n}=\\var{precround(s,3)}\\)</p>", "tags": [], "ungrouped_variables": ["a", "r", "n", "s"], "variables": {"r": {"name": "r", "definition": "random(0.1..0.9#0.1)", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "a": {"name": "a", "definition": "random(1..12#1)", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}, "s": {"name": "s", "definition": "({a})/(1-{r})", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "n": {"name": "n", "definition": "random(4..12#1)", "description": "", "group": "Ungrouped variables", "templateType": "randrange"}}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}