Question

4. Qual a solução da equação (x-1)+(x+2)+(x+5)+...+(x+47)=425?
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Answer 1

Resposta:

x = 2

Explicação passo a passo:

$a_1=x-1\\\\a_n=n+47\\\\r=x+2-(x-1)=x+2-x+1=3\\\\a_1+r(n-1)=a_n\\\\x-1+3(n-1)=x+47\\\\x-1+3n-3=x+47\\\\3n=47+4\\\\3n=51\\\\n=\frac{51}{3}=17\\\\\frac{(a_1+a_n).n}{2} =S_n\\\\\frac{(x-1+x+47).17}{2} =425\\\\\frac{(2x+46).17}{2}=425 \\\\(2x+46).17=850\\\\2x+46=50\\\\2x=50-46\\\\2x=4\\\\x=\frac{4}{2}\\\\x= 2$