In an arithmetic sequence, the common difference \(d\) is found by subtracting any term from the next term.
Let's calculate the common difference using the first two terms:
- First term: \( \frac{7}{4} \)
- Second term: \( \frac{3}{4} \)
Calculating \(d\): \[ d = \text{Second term} - \text{First term} = \frac{3}{4} - \frac{7}{4} = \frac{3 - 7}{4} = \frac{-4}{4} = -1 \]
We can also verify this with the next pairs of terms:
From \( \frac{3}{4} \) to \( -\frac{1}{4} \): \[ d = -\frac{1}{4} - \frac{3}{4} = -\frac{1 + 3}{4} = -\frac{4}{4} = -1 \]
From \( -\frac{1}{4} \) to \( -\frac{5}{4} \): \[ d = -\frac{5}{4} - \left( -\frac{1}{4} \right) = -\frac{5}{4} + \frac{1}{4} = -\frac{5 - 1}{4} = -\frac{4}{4} = -1 \]
Thus, the common difference \(d\) for the sequence is \( -1\).
So the answer is \( d = -1 \).