To find the common difference of the sequence \( \frac{7}{4}, \frac{3}{4}, -\frac{1}{4}, -\frac{5}{4} \), we need to subtract each term from the next term in the sequence.
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First pair:
\[ \frac{3}{4} - \frac{7}{4} = \frac{3-7}{4} = \frac{-4}{4} = -1 \] -
Second pair:
\[ -\frac{1}{4} - \frac{3}{4} = -\frac{1 + 3}{4} = -\frac{4}{4} = -1 \] -
Third pair:
\[ -\frac{5}{4} - \left(-\frac{1}{4}\right) = -\frac{5}{4} + \frac{1}{4} = \frac{-5 + 1}{4} = \frac{-4}{4} = -1 \]
The common difference between the terms of the sequence is \(-1\).