Given a geometric sequence where: a3 = –27 and a5 = –162
(a) determine the common ratio.
(b) find the rule for nth term of the sequence.
(c) find a8
(d) find s8

Part a.

We have

Dividing,

Ugh.  It would have killed them to choose a perfect square?

We can't really tell the sign on the common ratio; there's not enough information.  Let's just pick the positive square root going forward.

Part b

Part c

Part d

p(x)= 8 x³ - 36 x² + 54 x - 27

q(x) = 2 x -3

you can check your mistake and then you can choose the correct option.

dividend =   8 x³ - 36 x² + 54 x - 27

divisor = 2 x -3

if you want to find quotient, proceed as follows

q(x)= 0

2 x - 3=0

x =

now , i have used division method , to find quotient and remainder