// Numbas version: exam_results_page_options
{"name": "Fill in the gaps in an arithmetic sequence", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "metadata": {"description": "<p>Given arithmetic sequences with some terms missing, fill in the missing terms.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["m", "index"], "functions": {}, "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "statement": "<p>Fill in the gaps in the following arithmetic sequences.</p>", "preamble": {"js": "", "css": ""}, "tags": ["Arithmetic sequences", "arithmetic sequences", "sequences", "taxonomy"], "parts": [{"showFeedbackIcon": true, "marks": 0, "scripts": {}, "prompt": "<p>$\\var{m[0]*(index[0])}, \\; \\var{m[0]*(index[0]+1)}, \\; \\var{m[0]*(index[0]+2)}, \\;$&nbsp;[[0]] $, \\; \\var{m[0]*(index[0]+4)}, \\;$ [[1]]$, \\; \\var{m[0]*(index[0]+6)}$</p>\n<p><em></em></p>", "type": "gapfill", "gaps": [{"correctAnswerStyle": "plain", "scripts": {}, "maxValue": "{m[0]*(index[0]+3)}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "allowFractions": false, "minValue": "{m[0]*(index[0]+3)}", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false}, {"correctAnswerStyle": "plain", "scripts": {}, "maxValue": "{m[0]*(index[0]+5)}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "allowFractions": false, "minValue": "{m[0]*(index[0]+5)}", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}, {"showFeedbackIcon": true, "marks": 0, "scripts": {}, "prompt": "<p></p>\n<p>$\\var{m[1]*(index[1])}, \\; \\var{m[1]*(index[1]-1)}, \\;$&nbsp;[[0]]$, \\; \\var{m[1]*(index[1]-3)}, \\; \\var{m[1]*(index[1]-4)}, \\;$ [[1]] $, \\; \\var{m[1]*(index[1]-6)}$</p>", "type": "gapfill", "gaps": [{"correctAnswerStyle": "plain", "scripts": {}, "maxValue": "{m[1]*(index[1]-2)}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "allowFractions": false, "minValue": "{m[1]*(index[1]-2)}", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false}, {"correctAnswerStyle": "plain", "scripts": {}, "maxValue": "{m[1]*(index[1]-5)}", "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "allowFractions": false, "minValue": "{m[1]*(index[1]-5)}", "correctAnswerFraction": false, "variableReplacements": [], "mustBeReduced": false}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true}], "rulesets": {}, "variables": {"index": {"templateType": "anything", "definition": "shuffle(7..15 except 10)[0..2]", "description": "<p>Starting indices of the sequences.</p>", "group": "Ungrouped variables", "name": "index"}, "m": {"templateType": "anything", "definition": "shuffle(5..12 except 10)[0..2]", "description": "<p>Common differences of the sequences</p>", "group": "Ungrouped variables", "name": "m"}}, "advice": "<p>In an arithmetic sequence, the difference between two adjecent&nbsp;terms is always the same.</p>\n<h4>a)</h4>\n<p>The difference between the first two terms in this sequence is $\\var{m[0]*(index[0]+1)} - \\var{m[0]*(index[0])} = \\var{m[0]}$.</p>\n<p>So to get from one term to the next, add&nbsp;$\\var{m[0]}$.</p>\n<p>The complete sequence is&nbsp;</p>\n<p>\\[ \\var{m[0]*(index[0])}, \\; \\var{m[0]*(index[0]+1)}, \\; \\var{m[0]*(index[0]+2)}, \\; \\underline{\\var{m[0]*(index[0]+3)}}, \\; \\var{m[0]*(index[0]+4)}, \\; \\underline{\\var{m[0]*(index[0]+5)}}, \\; \\var{m[0]*(index[0]+6)} \\]</p>\n<h4>b)</h4>\n<p>The difference between the first two terms in this sequence is $\\var{m[1]*(index[1]-1)} - \\var{m[1]*(index[1])} = \\var{-m[1]}$.</p>\n<p>So to get from one term to the next, subtract&nbsp;$\\var{m[1]}$.</p>\n<p>The complete sequence is&nbsp;</p>\n<p>\\[ \\var{m[1]*(index[1])}, \\; \\var{m[1]*(index[1]-1)}, \\; \\underline{\\var{m[1]*(index[1]-2)}}, \\; \\var{m[1]*(index[1]-3)}, \\; \\var{m[1]*(index[1]-4)}, \\; \\underline{\\var{m[1]*(index[1]-5)}}, \\; \\var{m[1]*(index[1]-6)} \\]</p>\n<p><em></em></p>\n<p></p>\n<h4><em></em></h4>", "name": "Fill in the gaps in an arithmetic sequence", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}