Answer
Yes $r=\frac{3}{2}$
Work Step by Step
$2, 3, 4.5, 6.75, 10.125, 15.1875, . . .$
$\frac{a_2}{a_1}=\frac{3}{2}=r$
$ra_2=4.5=a_3$
$ra_3=6.75=a_4$
and so on. The sequence is geometric with common ratio $r=\frac{3}{2}$.
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