Solution (source code)

= Solution
{c}

Choose the <sequence>
$$
\boxed{b_n=(-1)^n n\qquad(n\geq1).}
$$
After every index there are positive terms arbitrarily large and negative terms arbitrarily small. Thus every term has both a larger later term and a smaller later term. The former excludes a <peak of a sequence> $(b_n)$, and the latter excludes a <peak of a sequence> $(-b_n)$.