Question 24Let $(a_n)$ and $(b_n)$ be sequences of numbers such that $a_0=50$, $b_0=27$, and for all $n\ge1$, $a_{n+1}=a_n+\dfrac1{b_n}$ and $b_{n+1}=b_n+\dfrac1{a_n}$. Find the smallest positive integer $k$ such that $a_k>100$.