Let ana_nan be a sequence defined by a1=1a_1=1a1=1, a2=1a_2=1a2=1, and an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2 for n>2n > 2n>2. What is the gcd(an,an+1)\text{gcd}(a_{n}, a_{n+1})gcd(an,an+1)?
an−1a_{n-1}an−1
111
ana_nan
222