my best interpretation of this is that you're given a geometric progression consisting of terms, the first of which is and the last of which is . (so we don't actually know right away how many terms there are.) the common ratio between terms is . you want to find the sum of all terms.
in a geometric progression, the -th term is determined by the previous term according to
starting with , we find
and so on. the general pattern for the -th term is then
the last term in the sequence is , so
the sum of these terms is given by
with and , we get a sum of
george washington hope this