Let [tex]a_n[/tex] be the [tex]n[/tex]-th term in the sequence. Consecutive terms have a fixed difference [tex]d[/tex] between them, i.e.
[tex]a_n - a_{n-1} = d[/tex]
for [tex]n>1[/tex]. By substitution, we have
[tex]a_{11} = a_{10} + d[/tex]
[tex]a_{12} = a_{11} + d = a_{10} + 2d[/tex]
[tex]a_{13} = a_{12} + d = a_{10} + 3d[/tex]
and so on. Notice how the subscript and coefficient of [tex]d[/tex] on the right side add up to the subscript on the left side. This means
[tex]a_{30} = a_{10} + 20d \implies 83 = 26 + 20d \implies d = \dfrac{57}{20}[/tex]
and
[tex]a_{50} = a_{10} + 40d = 26 + 40\cdot\dfrac{57}{20} = \boxed{140}[/tex]
