# What is the next fraction in this sequence? Simplify your answer. 2/3, 1/3, 1/6, 1/12

Feb 20, 2018

$\frac{1}{24}$

#### Explanation:

In this sequence, it seems that you divide the number by $2$ to get the next one in the sequence. Therefore, you would divide the last given number in the sequence, $\frac{1}{12}$, by $2$. Then it's just simple math.

$\frac{\frac{1}{12}}{2} = \left(\frac{1}{12}\right) \times \left(\frac{1}{2}\right) = \frac{1}{24}$

Feb 20, 2018

${a}_{5} = \frac{1}{24}$

#### Explanation:

$\text{these are the terms of a "color(blue)"geometric sequence}$

$a , a r , a {r}^{2} , a {r}^{3} , \ldots \ldots , a {r}^{n - 1}$

$\text{where a is the initial term and r is the common ratio}$

•color(white)(x)ar^(n-1)larrcolor(blue)"is the nth term"

•color(white)(x)r=a_2/a_1=a_3/a_2=...... =a^n/a^(n-1)

$\text{here } r = \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{\frac{1}{6}}{\frac{1}{3}} = \frac{\frac{1}{12}}{\frac{1}{6}} = \frac{1}{2}$

$\Rightarrow {a}_{5} = \frac{2}{3} \times {\left(\frac{1}{2}\right)}^{4} = \frac{2}{3} \times \frac{1}{16} = \frac{2}{48} = \frac{1}{24}$