Mathematics

An arithmetic progression is defined by a constant difference between consecutive terms—here that's $7$. Any term can be written as $a_n = 5 + (n-1) \cdot 7$ for some positive integer $n$. To check if $81$ belongs, you just need to solve for $n$ and see if you get a whole number; if $n$ isn't a positive integer, then $81$ isn't in the sequence.

An arithmetic progression is defined by a constant difference between consecutive terms—here that's $7$. Any term can be written as $a_n = 5 + (n-1) \cdot 7$ for some positive integer $n$. To check if $81$ belongs, you just need to solve for $n$ and see if you get a whole number; if $n$ isn't a positive integer, then $81$ isn't in the sequence.