If 8, $x$ and 18 are in continued proportion, the positive value of $x$ is:

Continued proportion means 8 : $x=x$ : 18, so $x^2=8\times 18=144$ and $x=12$ — the mean proportional between the two numbers. (Taking the ordinary average $(8+18)/2=13$ is the usual mistake; a mean proportional multiplies, it does not add.)