Problem

Source: 2023 Girls in Mathematics Tournament, Level A, Problem 1

Tags: arithmetic sequence, algebra, number theory



Define $(a_n)$ a sequence, where $a_1= 12, a_2= 24$ and for $n\geq 3$, we have: $$a_n= a_{n-2}+14$$a) Is $2023$ in the sequence? b) Show that there are no perfect squares in the sequence.