Question

Calcule a soma dos oito primeiros termos da P.G. (320, 160, 80,...).​

Answer 1

Soma da P.G:

Sₙ = a₁.(qⁿ-1)/q-1

a₁ = 320

a₂ = 160

q = a₂/a₁

q = 160/320

q = 1/2

$S_{8} = \frac{320((\frac{1}{2})^{8}-1) }{\frac{1}{2}-1 } \\\\S_{8} = \frac{320.(\frac{1}{256}-1) }{-\frac{1}{2} }\\\\S_{8} = 320.(-\frac{255}{256}).(-\frac{2}{1}) \\\\S_{8} = 640.(\frac{255}{256})\\\\S_{8} = 637,5$