$\underline{\text { Folklore }}$

The sequence $a_{n}$ is defined by the condition: $a_{n+1}=a_{n}-a_{n-1}$. Find $a_{100}$, if $a_{1}=3, a_{2}=7$.
Note that $a_{n+3}=a_{n+2}-a_{n+1}=-a_{n}$. Therefore, $a_{n+6}=a_{n}$, which means the terms of the sequence repeat with a period of 6. Since 100 divided by 6 leaves a remainder of 4, we have $a_{100}=a_{4}=-a_{1}$.

## Answer

$-3$.