examday

/TMUA

A real sequence $(a_n)$ satisfies

for every positive integer $n$. Which statements must be true?

• I. $a_{n+3}=-a_n$ for every positive integer $n$.
• II. $a_{n+6}=a_n$ for every positive integer $n$.
• III. $a_n+a_{n+1}+\cdots+a_{n+5}=0$ for every positive integer $n$.