// 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": [{"functions": {}, "ungrouped_variables": ["t1", "d", "t2", "t3", "t4", "tr", "tsum", "tans", "n"], "name": "Arithmetic Series 4", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "

To find the first term, we note that the $\\var{n}$th term is $\\simplify{{t1}+({n}-1)*{d}}$ and the common difference is $\\var{d}$ hence we can calculate the first term as $\\simplify{{t1}+({n}-1)*{d}}-(\\var{n}-1)\\times\\var{d}$

\n

\n

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 $i$th term of the arithmetic series. Since we know how to calculate $a_n$ from our above considerations, we know that $S_n = \\frac{n(a_1+a_1+(n-1)\\times d)}{2}$  which simplifies to $S_n = \\frac{n(2\\times\\var{t1}+(n-1)\\var{d})}{2}$

\n

", "rulesets": {}, "parts": [{"integerPartialCredit": 0, "prompt": "

Find the first term

", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{t1}", "minValue": "{t1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "prompt": "

Find the sum of the first $\\var{tsum}$ terms

", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{tans}", "minValue": "{tans}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "statement": "

The $\\var{n}$th term of an arithmetic series is $\\simplify{{t1}+({n}-1)*{d}}$

\n

The common difference is $\\var{d}$

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"tsum": {"definition": "random(11..29)", "templateType": "anything", "group": "Ungrouped variables", "name": "tsum", "description": ""}, "d": {"definition": "random(-9..9 except t1 except [1,0,-1])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "t2": {"definition": "t1+d", "templateType": "anything", "group": "Ungrouped variables", "name": "t2", "description": ""}, "t4": {"definition": "t1+3d", "templateType": "anything", "group": "Ungrouped variables", "name": "t4", "description": ""}, "tr": {"definition": "random(6..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "tr", "description": ""}, "t3": {"definition": "t1+2d", "templateType": "anything", "group": "Ungrouped variables", "name": "t3", "description": ""}, "t1": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "t1", "description": ""}, "n": {"definition": "random(4..20)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "tans": {"definition": "(tsum)/2*(2*t1+(tsum-1)*d)", "templateType": "anything", "group": "Ungrouped variables", "name": "tans", "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/"}]}