VTMO 2026 - Grade 9 - Semifinal - SET 1 - Self-study Question 24

Let $a_1,a_2,\ldots,a_n$ each be 1 or −1, and put $S_n=a_1a_2+a_2a_3+\cdots+a_na_1$. Can $S_n$ be zero in each case? Explain why. (a) n=30. (b) n=28.