Question

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

Answer 1

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