The second term is the first term, 45, times r, the common ratio.  
So the second term must be 45r.  So the sequence is

45, 45r, 1620

The third term is the second term, 45r, times r, the common ratio.  So the third term must be 45r².  But it's also 1620.

So we have the equation:



Divide both sides by 45



Take square roots of both sides:



So the second term 45r is 45(±6) or ±270.

The sequence is either

45, 270, 1620   or 45, -270, 1620.
 
Edwin