// Numbas version: exam_results_page_options
{"name": "Encontrar la diferencia com\u00fan en una Secuencia Aritm\u00e9tica", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "gaps": [{"allowFractions": false, "showFeedbackIcon": true, "maxValue": "{n[0]}", "variableReplacements": [], "minValue": "{n[0]}", "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0}], "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>$\\var{n[0]*index[0]}$, $\\var{n[0]*(index[0]+1)}$, $\\var{n[0]*(index[0]+2)}$, $\\var{n[0]*(index[0]+3)}$</p>\n<p>Diferencia Com&uacute;n=&nbsp;[[0]]</p>", "sortAnswers": false, "customMarkingAlgorithm": "", "type": "gapfill", "variableReplacementStrategy": "originalfirst"}, {"showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "gaps": [{"allowFractions": false, "showFeedbackIcon": true, "maxValue": "{n[1]}", "variableReplacements": [], "minValue": "{n[1]}", "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0}], "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>$\\var{n[1]*(index[1])}$, $?$,&nbsp;$\\var{n[1]*(index[1]+2)}$, $?$, $\\var{n[1]*(index[1]+4)}$</p>\n<p>Diferencia Com&uacute;n =&nbsp;[[0]]</p>", "sortAnswers": false, "customMarkingAlgorithm": "", "type": "gapfill", "variableReplacementStrategy": "originalfirst"}, {"showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "extendBaseMarkingAlgorithm": true, "gaps": [{"allowFractions": false, "showFeedbackIcon": true, "maxValue": "{n[2]}", "variableReplacements": [], "minValue": "{n[2]}", "marks": 1, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "mustBeReduced": false, "showCorrectAnswer": true, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0}], "unitTests": [], "showCorrectAnswer": true, "prompt": "<p>$\\var{n[2]*(index[2])}$, $?$, $?$, $\\var{n[2]*(index[2]+3)}$, $?$, $?$, $\\var{n[2]*(index[2]+6)}$</p>\n<p>diferencia Com&uacute;n =&nbsp;[[0]]</p>", "sortAnswers": false, "customMarkingAlgorithm": "", "type": "gapfill", "variableReplacementStrategy": "originalfirst"}], "statement": "<p>Encuentra las diferencias comunes de las siguientes secuencias aritm&eacute;ticas. Faltan algunos de los t&eacute;rminos.</p>", "ungrouped_variables": ["n", "index"], "extensions": [], "advice": "<p>En una secuencia aritm&eacute;tica, la diferencia entre dos t&eacute;rminos adyacentes es siempre la misma.</p>\n<p>Llame a la diferencia com&uacute;n $d$ y al primer t&eacute;rmino en la secuencia $a_0$. Entonces la secuencia es la siguiente:</p>\n<p>\\[ a_0, \\; a_0+d, \\; a_0+2d, \\; a_0+3d, \\; \\ldots \\]</p>\n<p>La diferencia entre un t&eacute;rmino en la secuencia y el t&eacute;rmino de lugar $n$&nbsp; es $n\\times d$.</p>\n<p>a)</p>\n<p>La diferencia entre los dos primeros t&eacute;rminos es $\\var{n[0]*(index[0]+1)} - \\var{n[0]*index[0]} = \\var{n[0]}$.</p>\n<p>As&iacute; que la diferencia com&uacute;n es $\\var{n[0]}$.</p>\n<h4>b)</h4>\n<p>No se nos da ning&uacute;n t&eacute;rmino adyacente de esta secuencia, pero se nos dan algunos t&eacute;rminos separados dos espacios.</p>\n<p>\\begin{align}<br/>2d &amp;= \\var{n[1]*(index[1]+2)} - \\var{n[1]*index[1]} \\\\<br/>&amp;= \\var{2*n[1]} \\\\<br/>d &amp;= \\var{n[1]}<br/>\\end{align}</p>\n<p>La diferencia com&uacute;n es $\\var{n[1]}$.</p>\n<h4>c)</h4>\n<p>Nuevamente, no tenemos t&eacute;rminos adyacentes de esta secuencia, pero tenemos dos t&eacute;rminos separados por tres lugares.</p>\n<p>\\begin{align}<br/>3d &amp;= \\var{n[2]*(index[2]+3)} - \\var{n[2]*index[2]} \\\\<br/>&amp;= \\var{3*n[2]} \\\\<br/>d &amp;= \\var{n[2]}<br/>\\end{align}</p>\n<p>La diferencia com&uacute;n es$\\var{n[2]}$.</p>\n<h4></h4>", "name": "Encontrar la diferencia com\u00fan en una Secuencia Aritm\u00e9tica", "metadata": {"description": "<p>Dadas las secuencias con t&eacute;rminos faltantes, encuentra la diferencia com&uacute;n entre los t&eacute;rminos.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "variable_groups": [], "variables": {"n": {"description": "", "definition": "shuffle(3..9)[0..3]", "templateType": "anything", "name": "n", "group": "Ungrouped variables"}, "index": {"description": "", "definition": "shuffle(5..15 except 10)[0..3]", "templateType": "anything", "name": "index", "group": "Ungrouped variables"}}, "functions": {}, "preamble": {"css": "", "js": ""}, "tags": [], "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}