a) 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 $m$.
b) 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 ${r^n} \gt 0.1$.
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