Question

How do I find the sum of this series?
Question D

Answer 1

sum of an infinite geometric sequence with the common ratio r, and the first term a1 is
`(a_1)/(1-r)`

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

`(-2)/(1-(-0.25))`=

`(-2)/(1+0.25)`=

`(-2)/(1.25)`=

`(-8)/(5)`=
the sum is -8/5 or -1.6