Question

What is the sum of the first 7 terms of the geometric series: -8 + (-4) + (-2) + 1 + 1/2+...

Answer 1

$a_1=-8;\ a_2=-4;\ r=a_2:a_1\to r=-4:(-8)=\dfrac{1}{2};\ n=7\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\subtitute:\\\\S_7=\dfrac{-8\left[1-\left(\dfrac{1}{2}\right)^7\right]}{1-\dfrac{1}{2}}=\dfrac{-8\left(1-\dfrac{1}{128}\right)}{\dfrac{1}{2}}\\\\=\dfrac{-8\cdot\dfrac{127}{128}}{\dfrac{1}{2}}=-\dfrac{127}{16}\cdot\dfrac{2}{1}=-\dfrac{127}{8}=-15\dfrac{7}{8}$