To find an equation that describes the sequence \(1, -5, 25, \ldots\), we first observe the terms:
- First term (\(a_1\)): \(1\)
- Second term (\(a_2\)): \(-5\)
- Third term (\(a_3\)): \(25\)
Now let's identify the pattern and derive a formula.
Looking at the terms, it seems that each term could be related to powers of \(-5\):
- The first term (\(n = 1\)) is \(1 = (-5)^0\).
- The second term (\(n = 2\)) is \(-5 = (-5)^1\).
- The third term (\(n = 3\)) is \(25 = (-5)^2\).
Generally, we can express the \(n\)-th term as follows:
\[ a_n = (-5)^{n-1} \]
Thus, the equation that describes the sequence is:
\[ a_n = (-5)^{n-1} \]
This formula accurately produces the sequence defined by the terms you provided.