Consider the sequence unu_nun defined by u1=1,u2=1u_1 = 1, u_2 = 1u1=1,u2=1, and un=3un−1−un−2u_{n} = 3u_{n-1} - u_{n-2}un=3un−1−un−2 for n>2n > 2n>2. Determine gcd(un,un+1)\text{gcd}(u_{n}, u_{n+1})gcd(un,un+1).
unu_nun
un−1u_{n-1}un−1
111
222