sum of an infinite geometric sequence with the common ratio r, and the first term a1 is [tex] \frac{a_1}{1-r} [/tex]
we notice
-2 times -1/4=1/2,
1/2 times -1/4=-1/8
so a1=-2
r=-1/4 or -0.25
so the sum is
[tex] \frac{-2}{1-(-0.25)} [/tex]=
[tex] \frac{-2}{1+0.25} [/tex]=
[tex] \frac{-2}{1.25} [/tex]=
[tex] \frac{-8}{5} [/tex]=
the sum is -8/5 or -1.6
