We are given the following sequence
[tex]\frac{2}{7},\frac{5}{14},\frac{3}{7},\frac{1}{2},\ldots[/tex]Let us check if there is a common difference between the consecutive terms
[tex]\begin{gathered} \frac{5}{14}-\frac{2}{7}=\frac{5-2(2)}{14}=\frac{5-4}{14}=\frac{1}{14} \\ \frac{3}{7}-\frac{5}{14}=\frac{2(3)-5}{14}=\frac{6-5}{14}=\frac{1}{14} \\ \frac{1}{2}-\frac{3}{7}=\frac{7(1)-2(3)}{14}=\frac{7-6}{14}=\frac{1}{14} \end{gathered}[/tex]As you can see, there is a common difference between the terms that is 1/14
If we add 1/14 to the last term of the sequence (1/2) then we would get the next fraction in the sequence.
[tex]undefined[/tex]