Find the general term of the sequence LaTeX: \displaystyle 5,\frac{15}{2},\frac{45}{4},\ldots

The common ratio is LaTeX: \displaystyle r=\frac{a_2}{a_1}=\frac{3}{2} . Using the first term and the common ratio gives LaTeX: \displaystyle a_n=5\left( \frac{3}{2} \right)^{n-1}