# How do you determine whether the sequence 1/3, 2/3, 1, 4/3, 5/6,... is arithmetic and if it is, what is the common difference?

Oct 14, 2017

$\textcolor{b l u e}{\frac{1}{3}}$

#### Explanation:

Concentrating on the first three values:

If a , b , c are in arithmetic sequence:

Then:

$b - a = c - b$

From example:

$\frac{2}{3} - \frac{1}{3} = 1 - \frac{2}{3} = \textcolor{b l u e}{\frac{1}{3}}$

So:

The common difference is $\textcolor{b l u e}{\frac{1}{3}}$