A sequence such that $(a_{n+1} - a_n )\rightarrow \infty $ but $(\sqrt{a_{n+1}} -\sqrt{a_n} )\rightarrow 0$

Does there exist a sequence $( a_n )_{n\ge 1}$ of positive real numbers such that $\lim _{n \rightarrow \infty}(a _{n+1}-a_n) =\infty $ and

$\lim _{n \rightarrow \infty}(\sqrt{a _{n+1}}-\sqrt{a_n}) =0 $ ?

I was thinking along this line :-

$(a _{n+1}-a_n)= (\sqrt{a _{n+1}}-\sqrt{a_n} ) (\sqrt{a _{n+1}}+\sqrt{a_n} ) =\frac 1{2^n}*3^n $

But succesive calculations to get $a_n$ gives no conclusions .

A trivial observations is $a_n$ must properly diverge to infinity . The answer is given to be yes. How may I proceed?