(a)[3]
The first two terms of an arithmetic progression are $161$ and $154$ respectively. The sum of the first $m$ terms is zero. Determine the value of $m$.
(b)[3]
A geometric progression with all terms positive has common ratio $r$. The sum of the first $n$ terms is below $90\%$ of the sum to infinity. Prove that $r^n > 0.1$.