The given sequence is: 1, 4, 16.
Let's analyze the terms:
- The first term is \(1\) (which is \(4^0\)),
- The second term is \(4\) (which is \(4^1\)),
- The third term is \(16\) (which is \(4^2\)).
From this, we can observe that the terms can be expressed as powers of \(4\).
The \(n\)-th term of the sequence can be expressed as: \[ a_n = 4^{n-1} \]
In the requested format, using decimals and integers, we can write:
\[ a_n = 4 \times (1)n-1 \]
Thus, the answer is: \[ a_n = 4 \cdot (1)n-1 \]