# Find the next term of the arithmetic sequence shown 1/6, 1/3, 1/2, 2/3

Find the next term of the arithmetic sequence shown 1/6, 1/3, 1/2, 2/3
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Lorenzo Aguilar
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
$\frac{2}{3}+\frac{1}{6}$
$=\frac{4}{6}+\frac{1}{6}=\frac{5}{6}$