To find an equation that describes the sequence \(-1, -4, -16, \ldots\), we need to analyze the pattern of the terms.
The sequence appears to be decreasing, and the terms suggest they can be expressed as powers of \(2\):
- The first term \(a_1 = -1 = -2^0\)
- The second term \(a_2 = -4 = -2^2\)
- The third term \(a_3 = -16 = -2^4\)
From this, we can see that the position \(n\) corresponds to the exponent being \(2(n - 1)\).
Putting this together, we can form the equation representing the \(n\)th term of the sequence:
\[ a_n = -2^{2(n - 1)} \]
So, the equation describing the sequence is:
\[ a_n = -2^{2(n - 1)} \]