// Numbas version: exam_results_page_options
{"name": "Sigma notation intro 3 - subscripts", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Sigma notation intro 3 - subscripts", "variable_groups": [], "metadata": {"description": "<p>Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "ungrouped_variables": ["a", "b", "f", "index"], "functions": {}, "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "statement": "<p>The following question is testing whether you understand the Sigma notation used in mathematics.</p>", "preamble": {"js": "", "css": ""}, "tags": [], "parts": [{"showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "prompt": "<p>The expression \\[\\sum_{\\var{index}=\\var{a}}^{\\var{b}}\\var{f}_{\\var{index}}\\] is equivalent to which of the following?</p>\n<p>[[0]]</p>", "gaps": [{"choices": ["<p>$\\var{f}_{\\var{a}}+\\var{f}_{\\var{a+1}}+\\var{f}_{\\var{a+2}}+\\ldots + \\var{f}_{\\var{b-2}}+ \\var{f}_{\\var{b-1}}+ \\var{f}_{\\var{b}}$</p>", "<p>$\\var{f}_{\\var{index}}+\\var{f}_{\\var{index}}+\\var{f}_{\\var{index}}+\\ldots +\\var{f}_{\\var{index}}+\\var{f}_{\\var{index}}+\\var{f}_{\\var{index}}$</p>", "<p>$\\var{a}+\\var{a+1}+\\var{a+2}+\\ldots + \\var{b-2}+ \\var{b-1}+ \\var{b}$</p>"], "maxMarks": 0, "scripts": {}, "minMarks": 0, "displayType": "radiogroup", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "1_n_2", "shuffleChoices": true, "showFeedbackIcon": true, "marks": 0, "displayColumns": "1", "matrix": ["1", 0, 0], "distractors": ["", "", ""], "variableReplacements": []}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "rulesets": {}, "advice": "<p>Sigma notation is used to represent a sum.</p>\n<p>In this sum, we are adding up a bunch of terms that look like $\\var{f}_{\\var{index}}$ each for a different value of the index $\\var{index}$. Notice the sum starts with $\\var{index}=\\var{a}$ and ends with $\\var{index}=\\var{b}$, therefore, \\[\\sum_{\\var{index}=\\var{a}}^{\\var{b}}\\var{f}_{\\var{index}}=\\var{f}_{\\var{a}}+\\var{f}_{\\var{a+1}}+\\var{f}_{\\var{a+2}}+\\ldots + \\var{f}_{\\var{b-2}}+ \\var{f}_{\\var{b-1}}+ \\var{f}_{\\var{b}}.\\]</p>", "variables": {"b": {"templateType": "anything", "definition": "a+random(50..79)", "description": "", "group": "Ungrouped variables", "name": "b"}, "index": {"templateType": "anything", "definition": "random(latex('i'),latex('j'),latex('k'),latex('r'),latex('s'),latex('n'),latex('m'))", "description": "", "group": "Ungrouped variables", "name": "index"}, "f": {"templateType": "anything", "definition": "random(latex('a'),latex('b'),latex('c'),latex('d'),latex('t'))", "description": "", "group": "Ungrouped variables", "name": "f"}, "a": {"templateType": "anything", "definition": "random(0..10)", "description": "", "group": "Ungrouped variables", "name": "a"}}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}