How to solve this determinant?

Question

How do I solve this determinant?

Answer 1

The determinant of a tridiagonal matrix can be calculated via the recurrence $f_n= af_{n-1} -cbf_{n-2}$ with $f_0=1$ and $f_1=a$

in this case $a=3,b=1,c=2$

so the recurrence relation is $f_n=3f_{n-1}-2f_{n-2}$