3.58: Surd rationalisation; marathon GP; AP–GP link

DO NOT USE A CALCULATOR. Write $\dfrac{16+11\sqrt{10}}{2+\sqrt{10}}+1$ in the form $p+q\sqrt{10}$, where $p$ and $q$ are integers.

Suzma runs $10$ km in week $1$, then $10\%$ more each week. Find least $n$ with total $>200$ km.

A GP has first term $a\neq0$ and ratio $r\neq1$. The $1$st, $2$nd, $3$rd GP terms are the $1$st, $3$rd, $7$th terms of an AP. Find $r$.