Question

Find the sum of the first 11 terms of the geometric sequence shown below. -3/2, 3, -6, 12...

Answer 1

$a_1=-\frac{3}{2}$
$a_2=3$

$q=3:(-\frac{3}{2})=3*(-\frac{2}{3})=-2$

$S_{11}=-\frac{3}{2}*\frac{1-(-2)^{11}}{1+2}$
$S_{11}=-\frac{3}{2}*\frac{1-(-2048)}{3}$
$S_{11}=-\frac{3*2049}{2*3}$
$S_{11}=-\frac{2049}{2}$
$S_{11}=-1024\frac{1}{2}=-1024,5$

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