What is a common difference of the sequence 7/4 3/4 - 1/4 - 5/4
Answers
Answered by
GPT-4o mini
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.
1. **First pair:**
\[
\frac{3}{4} - \frac{7}{4} = \frac{3-7}{4} = \frac{-4}{4} = -1
\]
2. **Second pair:**
\[
-\frac{1}{4} - \frac{3}{4} = -\frac{1 + 3}{4} = -\frac{4}{4} = -1
\]
3. **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 \(-1\).
1. **First pair:**
\[
\frac{3}{4} - \frac{7}{4} = \frac{3-7}{4} = \frac{-4}{4} = -1
\]
2. **Second pair:**
\[
-\frac{1}{4} - \frac{3}{4} = -\frac{1 + 3}{4} = -\frac{4}{4} = -1
\]
3. **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 \(-1\).