Limits Continuity And Differentiability

For every integer n, let a_n and b_n be real numbers. Let function f : R \(\to\) R be given by

\(f(x) = \left\{ {\matrix{ {{a_n} + \sin \pi x,} & {for\,x \in [2n,2n + 1]} \cr {{b_n} + \cos \pi x,} & {for\,x \in (2n - 1,2n)} \cr } } \right.\), for all integers n. If f is continuous, then which of the following hold(s) for all n ?