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{"name": "AF1 Sigma Notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "AF1 Sigma Notation", "tags": [], "metadata": {"description": "<p>Basic calculation from a sum given in Sigma notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate:</p>\n<p>\\[\\displaystyle{\\Sigma_{n=1}^3} \\var{b}n.\\]</p>\n<p></p>", "advice": "<p>The sigma notation $\\displaystyle<span class=\"enlighter-k0\">\\sum_</span><span class=\"enlighter-g1\">{</span><span class=\"enlighter-text\">n=</span><span class=\"enlighter-n1\">1</span><span class=\"enlighter-g1\">}</span><span class=\"enlighter-text\">^</span><span class=\"enlighter-g1\">{</span><span class=\"enlighter-k0\">3</span><span class=\"enlighter-g1\">}\\var{b}n$ is asking us to find the </span>sum of the first three terms of the sequence $\\var{b}n$<span class=\"enlighter-g1\">.&nbsp;</span></p>\n<p>\\[\\begin{split}\\Sigma_{n=1}^3 \\var{b}n &amp;\\, = (\\var{b}\\times 1) + (\\var{b}\\times 2) + (\\var{b}\\times 3) \\\\ &amp;\\, = \\var{b1} + \\var{b2} + \\var{b3} \\\\ &amp;\\, = \\var{sum}.\\end{split}\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Sigma\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise sigma notation.</a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "b*1", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "b*2", "description": "", "templateType": "anything", "can_override": false}, "b3": {"name": "b3", "group": "Ungrouped variables", "definition": "b*3", "description": "", "templateType": "anything", "can_override": false}, "sum": {"name": "sum", "group": "Ungrouped variables", "definition": "b1+b2+b3", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["b", "b1", "b2", "b3", "sum"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sum}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}]}]}], "contributors": [{"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}]}