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Determina la suma de las siguientes progresiones los primeros 18 términos de la progresión aritmética: an = -{4, 12, 20, 28, 36,,...}

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5 votes
Hello,
let
t=(-4)+(-12)+(-20)+(-28)+(-36)+....=-(4+12+20+28+36+...)=-s


a_(1)=4=-4+1*8

a_(2)=12=-4+2*8

a_(3)=20=-4+3*8

a_(4)=28=-4+4*8

...

a_(18)=?=-4+18*8=140


a_(i)=-4+i*8


s=\sum_(i=1)^(18) (-4+i*8)=\sum_(i=1)^(18) (-4)+\ 8*\sum_(i=1)^(18)(i)\\\\=(-4)*18+8*(1+2+3+4...+18)\\\\=-72+((1+18)*18)/(2)\\\\=-72+171=99


\boxed{\ t=-99}















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