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=========== 154 ===========

$\frac{10^{n-1}}{2^{n-2}} = \frac{10^{n-1}}{2^{n-1-1}} =\frac{10^{n-1}}{2^{n-1}\cdot2^{-1}} =2\cdot( \frac{10}{2} )^{n-1}=2\cdot5^{n-1}= \frac{2}{5} \cdot5^{n}\\\\ 5^n=24 \Rightarrow \frac{2}{5} \cdot5^{n}=\frac{2}{5} \cdot24=9.6$

=========== 155 ===========
$\frac{3^{n+2}}{12^{n+3}} = \frac{3^{n+2}}{3^{n+3} \cdot 4^{n+3}} =\frac{3^{n+2-n-3}}{(2^{n+3})^2} = \frac{1}{3\cdot(2^{n+3})^2} \\ 2^{n+3}= \frac{1}{6} \Rightarrow \frac{1}{3\cdot(2^{n+3})^2}= \frac{1}{3\cdot( \frac{1}{6} )^2}= \frac{1}{3\cdot \frac{1}{36}} =12$