To find the 25th term of the sequence \(-1, 3, 7, 11, \ldots\), we first need to identify the pattern.
We can observe the differences between the terms:
- \(3 - (-1) = 4\)
- \(7 - 3 = 4\)
- \(11 - 7 = 4\)
The sequence has a common difference of 4, which indicates it is an arithmetic sequence.
The formula for the \(n\)-th term of an arithmetic sequence can be expressed as:
\[ a_n = a_1 + (n-1)d \]
where:
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.
In this sequence:
- \(a_1 = -1\)
- \(d = 4\)
Now we can calculate the 25th term (\(a_{25}\)):
\[ a_{25} = -1 + (25-1) \cdot 4 \] \[ a_{25} = -1 + 24 \cdot 4 \] \[ a_{25} = -1 + 96 \] \[ a_{25} = 95 \]
Therefore, the 25th term is \(\boxed{95}\).