Find the common ratio of the following geometric sequence. if necessary, use the slash bar ( / ) to enter a fraction. reduce fractions to their lowest terms., 2/5 , -4/15 , 8/45 , -4/15 , -8/45

We have that
2/5 , -4/15 , 8/45 , -4/15 , -8/45

we know that
 
A geometric sequence is defined by   
a(n + 1) = r*a(n)
so
r = a(n + 1) / a(n)

Let
a1=2/5
a2=-4/15
a3=8/45

a2/a1=(-4/15)/(2/5)=-20/30> -2/3
a3/a2=(8/45)/(-4/15)=-20/30> -30/45> -2/3

the common ratio is
r=-2/3
calculate
a4=r*a3> (-2/3)*8/45> -16/135
a5=r*a4> (-2/3)*(-16/135)> 32/405

the correct geometric sequence is 
2/5 , -4/15 , 8/45 , -16/135 , 32/405,

the answer is
the common ratio is r=-2/3