# Find the nth term rule for 12,4,4/3,4/9,...

Find the nth term rule for $12,4,\frac{4}{3},\frac{4}{9},...$
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Kyle Delacruz
This is a GP which first term , a, of 12 and the common ratio ,r,of 3.
The common ratio is found from dividing any two consecutive terms..
$r=\frac{{T}_{2}}{{T}_{1}}=\frac{4}{12}=\frac{1}{3}$
The general term for any GP is ${T}_{n}=-a{r}^{n-1}$
Substituting the values for a and r we get..
${T}_{n}=12×{\left(\frac{1}{3}\right)}^{n-1}$