# How do you find the next term of the arithmetic sequence shown 1/6, 1/3, 1/2, 2/3?

Jun 28, 2018

$\frac{5}{6}$

#### Explanation:

fop we need to find the common difference between terms

$\frac{1}{6} , \frac{1}{3} , \frac{1}{2} , \frac{2}{3}$

$d = {a}_{2} - {a}_{1} = \frac{1}{3} - \frac{1}{6}$

$d = \frac{2}{6} - \frac{1}{6} = \frac{1}{6}$

that this is true for all adjacent terms is left for the reader to verify

the next term is therefore

$\frac{2}{3} + \frac{1}{6}$

$= \frac{4}{6} + \frac{1}{6} = \frac{5}{6}$