a) A geometric series is a series with a constant (common) ratio between successive terms. Therefore, if 160 is the first term and the second term is 240, then the common ratio is .
b) The th term of a geometric sequence with initial value and common ratio is given by . If we consider 1990 as the initial year, then and . Therefore, the number of units sold during 2002 will be given by the 13th term. Why do we use 13 instead of 12 (since 2002 is 12 years after 1990)? The question asks how many units will be sold during 2002, which includes the year 2002. Another way to word the question would be how many units will be sold by 2003. Returning to our formula for the nth term of a geometric sequence, the 13th term of our sequence is given by , which rounds to 20,759.
c) I believe you omitted the last few words of the question.