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

Feb 21, 2017

${T}_{n} = - \frac{4}{3} {\left(- 3\right)}^{n}$

#### Explanation:

${T}_{n} = a {r}^{n - 1}$ where ${T}_{n}$ = nth term, a = first term and r = common ratio.

$a = 4$ and $r = - \frac{12}{4} = - 3$,

${T}_{n} = 4 {\left(- 3\right)}^{n - 1}$

${T}_{n} = 4 {\left(- 3\right)}^{n} \cdot {\left(- 3\right)}^{-} 1 = 4 \left(- \frac{1}{3}\right) {\left(- 3\right)}^{n}$

${T}_{n} = - \frac{4}{3} {\left(- 3\right)}^{n}$