Geometric Progressions ratio

Question

I don't really know how to find the ratio of 3/2, any ideas? thanks!

Answer 1

Simply notice that each successive term is tripled the previous ($\times 3$) and then halved ($\times 1/2$). It's more a pattern-recognition thing than anything formal.

Of course, if you want, you can manually divide any $n^{th}$ term by the preceding term to also see the ratio in a geometric series. That would be the more proper way to demonstrate that the ratio of the series is $3/2$.