# How do you write the expression for the nth term of the geometric sequence a_1=6, r=-1/3, n=12?

Oct 2, 2017

$12$ th term is $\left(- \frac{2}{59049}\right)$

#### Explanation:

$n$ th term of geometric sequence is ${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$

${a}_{1} = 6 , r = - \frac{1}{3} , n = 12 \therefore {a}_{n} = 6 {\left(- \frac{1}{3}\right)}^{12 - 1}$ or

${a}_{n} = 6 {\left(- \frac{1}{3}\right)}^{11} = - \frac{6}{177147} = - \frac{2}{59049}$

$12$ th term is $\left(- \frac{2}{59049}\right)$ [Ans]