$n$ digit numbers are formed using the digits $1,2,3,4$ each of which begin with $1$ such that no two consecutive digits are same. If $a_n(n \ge 2)$ be such that $n$-digit numbers which ends in $1$ while $b_n$ be the ones which ends in a fixed number other than $1$, then the value of $a_7$ is?
I am in high school, have not been taught advanced mathematics and number theory. How to proceed with the question? I am struggling making a relation between $a_n$ and $b_n$.