// Numbas version: exam_results_page_options
{"name": "Arithmetic Series 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p>To find the common difference d&nbsp;we note that the $\\var{n1}$<sup>th</sup>&nbsp;term is $\\var{t1}$ and the $\\var{n2}$<sup>th&nbsp;</sup>term is $\\var{t2}$ so we can find the common difference d by noting $\\var{t2}-\\var{t1}=(\\var{n2}-\\var{n1})\\times d$, hence common difference $= \\var{d}$</p>\n<p>It is then straightforward to find the first term $a_1$ by substituting the common difference back into either of our given terms. For example, we know $\\var{t1} = a_1 + (\\var{n1}-1)\\times \\var{d}$, hence $a_1 = \\var{a}$</p>", "parts": [{"prompt": "<p>What is the first term and the common difference?</p>\n<p>First term$=$[[0]]</p>\n<p>Common difference$=$[[1]]</p>", "marks": 0, "gaps": [{"correctAnswerFraction": false, "minValue": "{a}", "variableReplacements": [], "showCorrectAnswer": true, "type": "numberentry", "integerPartialCredit": 0, "maxValue": "{a}", "allowFractions": false, "marks": 1, "integerAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false}, {"correctAnswerFraction": false, "minValue": "{d}", "variableReplacements": [], "showCorrectAnswer": true, "type": "numberentry", "integerPartialCredit": 0, "maxValue": "{d}", "allowFractions": false, "marks": 1, "integerAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showPrecisionHint": false}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "variable_groups": [], "ungrouped_variables": ["a", "d", "n1", "t1", "n2", "t2"], "rulesets": {}, "name": "Arithmetic Series 2", "tags": [], "type": "question", "functions": {}, "preamble": {"css": "", "js": ""}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "notes": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>In an arithmetic series, the $\\var{n1}$<sup>th&nbsp;</sup>term is $\\var{t1}$ and the $\\var{n2}$<sup>th&nbsp;</sup>term is $\\var{t2}$</p>\n<p></p>", "variables": {"d": {"templateType": "anything", "definition": "random(-9..9 except a except [1,0,-1]) ", "description": "", "group": "Ungrouped variables", "name": "d"}, "t1": {"templateType": "anything", "definition": "a+(n1-1)*d", "description": "", "group": "Ungrouped variables", "name": "t1"}, "n1": {"templateType": "anything", "definition": "random(4..19)", "description": "", "group": "Ungrouped variables", "name": "n1"}, "n2": {"templateType": "anything", "definition": "random(4..19 except n1)", "description": "", "group": "Ungrouped variables", "name": "n2"}, "a": {"templateType": "anything", "definition": "random(2..9)", "description": "", "group": "Ungrouped variables", "name": "a"}, "t2": {"templateType": "anything", "definition": "a+(n2-1)*d", "description": "", "group": "Ungrouped variables", "name": "t2"}}, "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/"}]}