The formula for the sum of the first "n" terms of any geometric progression


     = 


(where "q" is the common ratio) can be written in an equivalent form 


     = .


So, with the given data,


    1533 = ,


or, simplifying


    768*q - 3 = 1533*(q-1)

    768q - 3 = 1533q - 1533

    1533 - 3 = 1533q - 768q

    1530 = 765q

    q =  = 2.


So, the common ratio is just found: it is 2.


Next,  to find "n", the number of terms, use the general formula for the n-th term


    768 = 

     =  = 256

    ============>  n - 1 = 8;  hence,  n = 9.


ANSWER.  The number of terms is 9 and the common ratio is 2.