The given sequence is 1, 4, 16, ...
To analyze the sequence, we can identify the pattern between the terms:
- The first term \( a_1 = 1 = 2^0 \)
- The second term \( a_2 = 4 = 2^2 \)
- The third term \( a_3 = 16 = 2^4 \)
We notice that the exponents are \(0, 2, 4\), which can be described as \(2(n-1)\) where \(n\) is the position of the term in the sequence.
Thus, we can express the nth term \( a_n \) in the following way:
\[ a_n = 2^{2(n-1)} \]
Therefore, the equation describing the sequence is:
\[ a_n = 2^{2(n-1)} \]