Question

what is the next fraction in this sequence? simplify your answer.
\frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, ...

Explanation:

Step1: Find the common difference

First, rewrite the fractions with a common denominator (6) to see the pattern:
$\frac{1}{6}$, $\frac{2}{6}$, $\frac{3}{6}$, $\frac{4}{6}$, ...
The difference between consecutive terms is $\frac{2}{6} - \frac{1}{6} = \frac{1}{6}$, $\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$, etc. So the common difference $d = \frac{1}{6}$.

Step2: Calculate the next term

The last given term is $\frac{2}{3} = \frac{4}{6}$. Add the common difference:
$\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$.

Answer:

$\frac{5}{6}$