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"showpreview": true, "answer": "(1/2)*{upsum0}*{coeff[0]}*(1+{upsum0})", "checkvariablenames": false}], "scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "marks": 0, "variableReplacements": [], "prompt": "<p>$\\sum\\limits_{n=1}^\\var{upsum0} \\var{coeff[0]}n =$[[0]]$+$[[1]]$+$[[2]]$+$[[3]]$+$[[4]]$+$[[5]]$=$[[6]]</p>"}, {"variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrangepoints": 5, "marks": "0.5", "showCorrectAnswer": true, "answersimplification": "all", "variableReplacementStrategy": "originalfirst", "scripts": {}, "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "showpreview": true, "answer": "{coeff[1]}", "checkvariablenames": false}, {"vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrangepoints": 5, "marks": "0.5", "showCorrectAnswer": true, "answersimplification": "all", "variableReplacementStrategy": "originalfirst", "scripts": {}, "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "showpreview": true, "answer": "{coeff[1]}+1", "checkvariablenames": false}, {"vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrangepoints": 5, "marks": "0.5", "showCorrectAnswer": true, "answersimplification": "all", "variableReplacementStrategy": "originalfirst", "scripts": {}, "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "showpreview": true, "answer": "{coeff[1]}+2", "checkvariablenames": false}, {"vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrangepoints": 5, "marks": 1, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "expectedvariablenames": [], "variableReplacements": [], "type": "jme", "showpreview": true, "answer": "{coeff[1]}+3", "checkvariablenames": false}, {"vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkingtype": "absdiff", "vsetrangepoints": 5, 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"", "licence": "Creative Commons Attribution 4.0 International", "description": ""}, "statement": "<p>Evaluate each of these</p>", "functions": {}, "ungrouped_variables": ["upsum0", "coeff", "pow", "low", "upsum1"], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"low": {"templateType": "anything", "name": "low", "description": "", "group": "Ungrouped variables", "definition": "shuffle(2..4)"}, "upsum1": {"templateType": "anything", "name": "upsum1", "description": "", "group": "Ungrouped variables", "definition": "4"}, "upsum0": {"templateType": "anything", "name": "upsum0", "description": "", "group": "Ungrouped variables", "definition": "6"}, "pow": {"templateType": "anything", "name": "pow", "description": "", "group": "Ungrouped variables", "definition": "shuffle(2..4)"}, "coeff": {"templateType": "anything", "name": "coeff", "description": "", "group": "Ungrouped variables", "definition": "shuffle(2..9)"}}, "preamble": {"js": "", "css": ""}, "tags": [], "variable_groups": [], "type": "question", "advice": "<p>a) $(1/2)*\\var{upsum0}*\\var{coeff[0]}*(1+\\var{upsum0})$, here we used that the sum of the first $n$ terms in an arithmetic sequence is $\\frac{n(a+l)}{2}$ where $a$ is the first term and $l$ is the $n$<sup>th</sup> term.&nbsp;</p>\n<p></p>", "question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "showQuestionGroupNames": false, "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}