(a) An arithmetic sequence $a_1, a_2, a_3, \ldots$ has common difference $d$, where $d<0$. The sum of the first $n$ terms of the sequence is denoted by $S_n$. Given that $\left|a_8\right|=\left|a_{13}\right|$, find the value of $n$ for which $S_n$ is maximum.


(b) The terms $u_1, u_2$ and $u_3$ are three consecutive terms of a geometric progression. It is given that
$u_1, u_2$ and $u_3-32$
form an arithmetic progression, and that
$u_1, u_2-4$ and $u_3-32$
form another geometric progression. Find the possible values of $u_1, u_2$ and $u_3$.