import{E as $,r,h as o,w as n}from"./index-hc8lvKav.js";const m="Somme des termes d'une suite arithmétique",u=!0,h="mathLive",p="30/11/2021",d="cfac9",l="1N12";class S extends ${constructor(){super(),this.typeExercice="simple",this.nbQuestions=2,this.spacingCorr=1.5,this.consigneCorrection="Rappel : $1 + 2 + 3 + ... + n = \\dfrac{n(n + 1)}{2}$"}nouvelleVersion(){const t=r(1,10),i=r(3,10),e=r(2,4)*10,s=o(["u","v","w"]);this.question=`Soit $${s}$ la suite arithmétique de premier terme $${s}_0 = ${t}$ et de raison $${i}$.`,this.question+=`<br>Calculer $\\displaystyle S = ${s}_0 + ${s}_1 + ... + ${s}_{${e}} =\\sum_{k=0}^{k=${e}}${s}_k$.`,this.reponse=(e+1)*(t+t+e*i)/2,this.correction=`$S = ${t} + (${t} + ${i}) + (${t} + 2\\times${i}) + ... + (${t} + ${e} \\times ${i})$`,this.correction+=`<br>$\\phantom{S} = (\\underbrace{${t} + ${t} + ... + ${t}}_{${e+1}\\times ${t}}) + ${i} \\times (1 + 2 + ... + ${e})$`,this.correction+=`<br>$\\phantom{S} = ${e+1} \\times ${t} + ${i} \\times \\dfrac{${e}\\times${e+1}}{2}$`,this.correction+=`<br>$\\phantom{S} = ${n(this.reponse)}$`}}export{p as dateDePublication,S as default,u as interactifReady,h as interactifType,l as ref,m as titre,d as uuid};
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