Geometric Sequence

The common difference between terms is $\frac{\frac{1}{4}}{16}=\frac{1}{64}$.

The 30th term is 30-24=6 terms away, meaning 6 common differences from 24.

So, the 30th term is $\frac{1}{4}*{(\frac{1}{64})}^6$, $\frac{1}{{2}^{2}}*\frac{1}{{2}^{36}}=\frac{1}{{2}^{38}}$, is our final answer.