To find the 25th term of the sequence \(-1, 3, 7, 11, \ldots\), we first need to identify the pattern in the sequence.
The sequence can be analyzed as follows:
- The first term (\(a_1\)) is \(-1\).
- The second term (\(a_2\)) is \(3\).
- The third term (\(a_3\)) is \(7\).
- The fourth term (\(a_4\)) is \(11\).
We can notice the differences between the consecutive terms:
- \(3 - (-1) = 4\)
- \(7 - 3 = 4\)
- \(11 - 7 = 4\)
The common difference is \(4\). Since this is an arithmetic sequence, we can use the formula for the \(n\)-th term of an arithmetic sequence:
\[ a_n = a_1 + (n-1)d \]
where:
- \(a_1\) is the first term,
- \(d\) is the common difference,
- \(n\) is the term number.
Substituting the known values into the formula:
\[ a_n = -1 + (n-1) \cdot 4 \]
Now, we need to find the 25th term (\(a_{25}\)):
\[ a_{25} = -1 + (25-1) \cdot 4 \] \[ = -1 + 24 \cdot 4 \] \[ = -1 + 96 \] \[ = 95 \]
Thus, the 25th term of the sequence is \(95\).
The correct answer is \(\boxed{95}\).
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