Which of the following is the correct definition of a geometric sequence?

Geometric sequences use multiplication as the common ratio, whether you are dividing by a fraction or a rational number.  The key thing is that the ratio has to be the same throughout the whole sequence.  Therefore, that makes the last choice above the one you want.

In the given question it is already mentioned that a 64 gallon tank contains 45 gallons of oil. Out of the 45 gallons 4/5 th of the quantity is sold. It can be said that the full tank capacity of 64 gallons is of no use to the problem.
Now getting to the equation part of the problem.
Quantity of oil removed = (4/5) * 45 gallons
                                       = (4 * 9) gallons
                                     = 36 gallons.
So it can be said that 36 gallons of oil from the total of 45 gallons has been sold.