{"version":3,"file":"1N12-1-VLdwzICO.js","sources":["../../src/exercices/1e/1N12-1.js"],"sourcesContent":["import { texteGras } from '../../lib/format/style'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport { randint } from '../../modules/outils.js'\nexport const titre = 'Calculer une somme'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\n\nexport const dateDePublication = '28/12/2022'\n\n/**\n *\n * @author Rémi Angot\n * Référence 1N14\n*/\nexport const uuid = '8ed19'\nexport const ref = '1N12-1'\nexport default class SommeSuite extends Exercice {\n  constructor () {\n    super()\n    this.typeExercice = 'simple'\n    this.nbQuestions = 1\n    this.spacingCorr = 2\n  }\n\n  nouvelleVersion () {\n    const u0 = randint(2, 10)\n    const r = randint(2, 8)\n    const n = randint(12, 30)\n    this.question = `Calculer $S = ${u0} + ${u0 + r} + ${u0 + 2 * r} + ${u0 + 3 * r} + ... + ${u0 + n * r}$.`\n    this.reponse = (n + 1) * (u0 + u0 + n * r) / 2\n    this.correction = `$S = ${u0} + (${u0} + ${r}) + (${u0} + 2 \\\\times ${r}) + (${u0} + 3 \\\\times ${r}) + ... + (${u0} + ${n} \\\\times ${r})$`\n    this.correction += `<br>$S = (\\\\underbrace{${u0} + ${u0} + ${u0} + ... + ${u0}}_{${n + 1}\\\\times${u0}}) + ${r} \\\\times (1 + 2 + 3 + ... + ${n})$`\n    this.correction += '<br> Or, on sait d\\'après le cours que : $1 + 2 + 3 + ... + n = \\\\dfrac{n(n+1)}{2}$.'\n    this.correction += `<br>$S = ${n + 1} \\\\times ${u0} + ${r} \\\\times \\\\dfrac{${n} \\\\times ${n + 1}}{2}$`\n    this.correction += `<br>$S = ${texNombre(this.reponse)}$`\n    this.correction += `<br><br>${texteGras('Autre méthode')} : on reconnait la somme des $${n + 1}$ premiers termes d'une suite arithmétique de premier terme $${u0}$ et de raison $${r}$.`\n    this.correction += '<br>Donc d\\'après le cours :'\n    this.correction += `<br>$S=(\\\\text{nombre de termes})\\\\times\\\\dfrac{\\\\text{premier terme} + \\\\text{dernier terme}}{2}=${n + 1}\\\\times\\\\dfrac{${u0} + ${u0 + n * r}}{2}=${texNombre(this.reponse)}$.`\n  }\n}\n"],"names":["titre","interactifReady","interactifType","dateDePublication","uuid","ref","SommeSuite","Exercice","u0","randint","r","n","texNombre","texteGras"],"mappings":"8FAIY,MAACA,EAAQ,qBACRC,EAAkB,GAClBC,EAAiB,WAEjBC,EAAoB,aAOpBC,EAAO,QACPC,EAAM,SACJ,MAAMC,UAAmBC,CAAS,CAC/C,aAAe,CACb,MAAO,EACP,KAAK,aAAe,SACpB,KAAK,YAAc,EACnB,KAAK,YAAc,CACpB,CAED,iBAAmB,CACjB,MAAMC,EAAKC,EAAQ,EAAG,EAAE,EAClBC,EAAID,EAAQ,EAAG,CAAC,EAChBE,EAAIF,EAAQ,GAAI,EAAE,EACxB,KAAK,SAAW,iBAAiBD,CAAE,MAAMA,EAAKE,CAAC,MAAMF,EAAK,EAAIE,CAAC,MAAMF,EAAK,EAAIE,CAAC,YAAYF,EAAKG,EAAID,CAAC,KACrG,KAAK,SAAWC,EAAI,IAAMH,EAAKA,EAAKG,EAAID,GAAK,EAC7C,KAAK,WAAa,QAAQF,CAAE,OAAOA,CAAE,MAAME,CAAC,QAAQF,CAAE,gBAAgBE,CAAC,QAAQF,CAAE,gBAAgBE,CAAC,cAAcF,CAAE,MAAMG,CAAC,YAAYD,CAAC,KACtI,KAAK,YAAc,0BAA0BF,CAAE,MAAMA,CAAE,MAAMA,CAAE,YAAYA,CAAE,MAAMG,EAAI,CAAC,UAAUH,CAAE,QAAQE,CAAC,+BAA+BC,CAAC,KAC7I,KAAK,YAAc,sFACnB,KAAK,YAAc,YAAYA,EAAI,CAAC,YAAYH,CAAE,MAAME,CAAC,oBAAoBC,CAAC,YAAYA,EAAI,CAAC,QAC/F,KAAK,YAAc,YAAYC,EAAU,KAAK,OAAO,CAAC,IACtD,KAAK,YAAc,WAAWC,EAAU,eAAe,CAAC,iCAAiCF,EAAI,CAAC,gEAAgEH,CAAE,mBAAmBE,CAAC,KACpL,KAAK,YAAc,8BACnB,KAAK,YAAc,qGAAqGC,EAAI,CAAC,kBAAkBH,CAAE,MAAMA,EAAKG,EAAID,CAAC,QAAQE,EAAU,KAAK,OAAO,CAAC,IACjM,CACH"}