The 4th term of an AP is 0. What is the ratio of its 22nd term to its 10th term?

$a_4=a+3d=0$ gives $a=-3d$. Then $a_{22}=-3d+21d=18d$ and $a_{10}=-3d+9d=6d$, so the ratio is 18$d:6d=3$ : 1. The tempting 2 : 1 comes from assuming any such pair doubles; 11 : 5 just reduces the term numbers 22 : 10, which is not how terms behave.