Find the next three terms in the geometric sequence:

6075 / 4050  =  2/3

4050 / 2700  =  2/3

2700 / 1800  =  2/3

Find  2/3  or 1800  for the next term; then find 2/3rds of that answer for the next term, etc.

Find the next three terms in the geometric sequence: 

6075,4050,2700,1800

$\text{ratio } r = \frac{4050}{6075} = \frac{2700}{4050} = \frac{1800}{2700} = \frac23$

$a_4 = 1800 \\ a_5 = a_4 \cdot r = 1800\cdot \frac23 = 1200 \\ a_6 = a_5 \cdot r = 1200\cdot \frac23 = 800 \\ a_7 = a_6 \cdot r = 800\cdot \frac23 = 533.\bar{3} \\$