# How do you write the expression for the nth term of the sequence given 1/3, 2/9, 4/27, 8/81,...?

${a}_{n} = {2}^{n - 1} / {3}^{n}$
First look at the bottom and see how it is increasing. $3 , 9 , 21 , 81$. Looks like for each number it increases, it is $3$ to the something power, so we have ${3}^{n}$. Now we will look at the top and try and guess what causes $1 , 2 , 4 , 8$. Look's like it is $2$ to the something power, except for $1$, so it must going to the $0$ power, in order for it to turn $0$. Now we have ${2}^{n - 1}$
This is why we have: ${a}_{n} = {2}^{n - 1} / {3}^{n}$