Find anfor this sequence:
5, 6, 7, 5, 6, 7, 5, 6, 7, ...
you can use a piece-wise definition: $\displaystyle a_n = \left \{ \begin{matrix} 5 & \text{ if } n \equiv 1 \bmod 3 \\ 6 & \text{ if } n \equiv 2 \bmod 3 \\ 7 & \text{ if } n \equiv 0 \bmod 3 \end{matrix} \right.$
are you familiar with the notation $\displaystyle n \equiv m \bmod 3$? It means $\displaystyle n = m + 3k$ for some integer $\displaystyle k$