Filling Question
Given a sequence satisfying the condition
a_{n+2}+a_n=a_{n+1} and a_1=2 and a_2=3, then a_{2007}=
Given a sequence satisfying the condition
a_{n+2}+a_n=a_{n+1} and a_1=2 and a_2=3, then a_{2007}=
a_{n+2}=a_{n+1}-a_n
a_{n+3}=a_{n+2}-a_{n+1}
Addition of two expressions , we get
a_{n+3}=-a_n
Therefore
a_{n+6}=a_n
So the terms of this sequence has a period of 6 and repeat themselves every 6 terms.
a_{2017} = a_{336\times 6+1} =a_1 = 2