// Numbas version: exam_results_page_options
{"name": "Arithmetic Series 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"tans": {"name": "tans", "group": "Ungrouped variables", "definition": "(tsum)/2*(2*t1+(tsum-1)*d)", "description": "", "templateType": "anything"}, "t3": {"name": "t3", "group": "Ungrouped variables", "definition": "t1+2d", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(4..20)", "description": "", "templateType": "anything"}, "tsum": {"name": "tsum", "group": "Ungrouped variables", "definition": "random(11..29)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9..9 except t1 except [1,0,-1])", "description": "", "templateType": "anything"}, "tr": {"name": "tr", "group": "Ungrouped variables", "definition": "random(6..10)", "description": "", "templateType": "anything"}, "t1": {"name": "t1", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}, "t4": {"name": "t4", "group": "Ungrouped variables", "definition": "t1+3d", "description": "", "templateType": "anything"}, "t2": {"name": "t2", "group": "Ungrouped variables", "definition": "t1+d", "description": "", "templateType": "anything"}}, "showQuestionGroupNames": false, "ungrouped_variables": ["t1", "d", "t2", "t3", "t4", "tr", "tsum", "tans", "n"], "variablesTest": {"condition": "", "maxRuns": 100}, "name": "Arithmetic Series 4", "parts": [{"allowFractions": false, "integerAnswer": true, "integerPartialCredit": 0, "maxValue": "{t1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerFraction": false, "showCorrectAnswer": true, "prompt": "<p>Find the first&nbsp;term</p>", "showPrecisionHint": false, "scripts": {}, "minValue": "{t1}", "marks": 1, "type": "numberentry"}, {"allowFractions": false, "integerAnswer": true, "integerPartialCredit": 0, "maxValue": "{tans}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "correctAnswerFraction": false, "showCorrectAnswer": true, "prompt": "<p>Find the sum of the first $\\var{tsum}$ terms</p>", "showPrecisionHint": false, "scripts": {}, "minValue": "{tans}", "marks": 1, "type": "numberentry"}], "rulesets": {}, "variable_groups": [], "statement": "<p>The $\\var{n}$<sup>th&nbsp;</sup>term of an arithmetic series is $\\simplify{{t1}+({n}-1)*{d}}$</p>\n<p>The common difference is $\\var{d}$</p>", "metadata": {"description": "", "notes": "", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "tags": [], "advice": "<p>To find the first<sup>&nbsp;</sup>term, we note that the $\\var{n}$<sup>th</sup> term is $\\simplify{{t1}+({n}-1)*{d}}$ and the common difference is $\\var{d}$&nbsp;hence we can calculate the first&nbsp;term as $\\simplify{{t1}+({n}-1)*{d}}-(\\var{n}-1)\\times\\var{d}$</p>\n<p></p>\n<p>To find the sum of the first $\\var{tsum}$ terms we used the known formula $S_n = \\frac{n(a_1 + a_n)}{2}$ where $a_i$ is the $i$<sup>th</sup> term of the arithmetic series. Since we know how to calculate $a_n$ from our above considerations, we know that $S_n = \\frac{n(a_1+a_1+(n-1)\\times d)}{2}$ &nbsp;which simplifies to $S_n = \\frac{n(2\\times\\var{t1}+(n-1)\\var{d})}{2}$</p>\n<p></p>", "functions": {}, "question_groups": [{"name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": []}], "type": "question", "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/"}]}