# How do you rewrite each explicit formula in function form g_n=-6*(1/3)^(n-1)?

Jan 13, 2018

The geometric sequence is $- 6 , - 2 , - \frac{2}{3} , - \frac{2}{9} \ldots .$

#### Explanation:

${g}_{n} = - 6 {\left(\frac{1}{3}\right)}^{n - 1}$

${g}_{1} = - 6 {\left(\frac{1}{3}\right)}^{1 - 1} = - 6 \cdot 1 = - 6$

${g}_{2} = - 6 {\left(\frac{1}{3}\right)}^{2 - 1} = - 6 \cdot \frac{1}{3} = - 2$

${g}_{3} = - 6 {\left(\frac{1}{3}\right)}^{3 - 1} = - 6 \cdot {\left(\frac{1}{3}\right)}^{2} = - \frac{2}{3}$

${g}_{4} = - 6 {\left(\frac{1}{3}\right)}^{4 - 1} = - 6 \cdot {\left(\frac{1}{3}\right)}^{3} = - \frac{2}{9}$

The geometric sequence is $- 6 , - 2 , - \frac{2}{3} , - \frac{2}{9} \ldots .$

First term is ${g}_{1} = - 6$ , common ratio is $r = - \frac{1}{3}$ [Ans]