Find the missing term The sequence $10000, 121, 100, 31, 24, n, 20$ represents a number $x$ with respect to different bases. What is the missing number, $n$?
This is from my elementary computer aptitude paper. Is there any way to solve this quickly?

Assuming the bases are in ascending order with a difference of 1, and the first one is in base $b$, then $$b^4=(b+2)^2$$
and so $$b^2=b+2$$
from which we can conclude that $b=2$ and the number is 16, which in base 7 is represented as 22.
