(Tsinghua 2017.4.29 Standard Academic Ability Test 20)
Given the sequence $\{a_n\}$, where $a_1=a$, $a_2=b$, $a_{n+2}=a_n-\dfrac 7{a_{n+1}}$, then _______
A.$\{a_n\}$ may increase
B.$\{a_n\}$ may decrease
C.$\{a_n\}$ may be finite
D.$\{a_n\}$ may be infinite
Answer: C and D, Hint: AB must have a limit according to monotone bounding, exclude, C, D can be determined according to $ab+7$ whether $=7k,k\in N$