// 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": [{"functions": {}, "ungrouped_variables": ["a", "d", "n1", "t1", "n2", "t2"], "name": "Arithmetic Series 2", "tags": [], "preamble": {"css": "", "js": ""}, "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>", "rulesets": {}, "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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{a}", "minValue": "{a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{d}", "minValue": "{d}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "d": {"definition": "random(-9..9 except a except [1,0,-1]) ", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "t2": {"definition": "a+(n2-1)*d", "templateType": "anything", "group": "Ungrouped variables", "name": "t2", "description": ""}, "t1": {"definition": "a+(n1-1)*d", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}, "n1": {"definition": "random(4..19)", "templateType": "anything", "group": "Ungrouped variables", "name": "n1", "description": ""}, "n2": {"definition": "random(4..19 except n1)", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}]}], "contributors": [{"name": "joshua boddy", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/557/"}]}