The first and second terms of an arithmetic progression are 161 and 154 respectively. The sum of the first \(m\) terms is zero. Find the value of \(m\).
A geometric progression, in which all the terms are positive, has common ratio \(r\). The sum of the first \(n\) terms is less than \(90 \%\) of the sum to infinity. Show that \(r ^ { n } > 0.1\).