# How do you find the nth term rule for 12,4,4/3,4/9,...?

Jul 18, 2016

${T}_{n} = 12 \times {\left(\frac{1}{3}\right)}^{n - 1}$

#### Explanation:

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..

$r = {T}_{2} / {T}_{1} = \frac{4}{12} = \frac{1}{3}$

The general term for any GP is ${T}_{n} = - a {r}^{n - 1}$

Substituting the values for a and r we get..

${T}_{n} = 12 \times {\left(\frac{1}{3}\right)}^{n - 1}$