Consider the sequence $$a_{n} = \dfrac{n\cos(n\pi)}{2n-1}.$$ Write the first five terms of $a_{n}$, and find $\lim_{n\rightarrow\infty}a_{n}$. If the sequence diverges, enter "divergent" in the answer box for its limit.

a) First five terms: ,,,,.
b) $\lim_{n\rightarrow\infty}a_{n} =$ .