# How do you write an equation for the nth term of the geometric sequence 36,12,4...?

Oct 14, 2016

${t}_{n} = a \times {r}^{n - 1}$

We can determine the value of $r$ by using the formula $r = {t}_{2} / {t}_{1}$.

$r = {t}_{2} / {t}_{1} = \frac{12}{36} = \frac{1}{3}$

So,

${t}_{n} = 36 \times {\left(\frac{1}{3}\right)}^{n - 1}$

Hopefully this helps!