`(1)/(4)" " (1)/(2) " "(3)/(4)" "1" "1(1)/(4)" "1(1)/(2)" "1(3)/(4) ?`

Options

A. 2
B. 4
C. 6
D. `1(1)/(5)`

Explanation

To solve the series `(1/4), (1/2), (3/4), 1, 1(1/4), 1(1/2), 1(3/4)`, we need to identify the pattern in the series and find the next term.

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions**:
- The mixed numbers in the series are `1(1/4)`, `1(1/2)`, and `1(3/4)`.
- Convert these to improper fractions:
- `1(1/4) = 1 + 1/4 = 4/4 + 1/4 = 5/4`
- `1(1/2) = 1 + 1/2 = 4/4 + 2/4 = 6/4`
- `1(3/4) = 1 + 3/4 = 4/4 + 3/4 = 7/4`

So the series now looks like:
\[ \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{6}{4}, \frac{7}{4} \]

2. **Identify the Pattern**:
- The series can be rewritten as:
\[ \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4}, \frac{6}{4}, \frac{7}{4} \]
- We can see that each term increases by \(\frac{1}{4}\).

3. **Calculate the Next Term**:
- The last term we have is \(\frac{7}{4}\).
- To find the next term, we add \(\frac{1}{4}\) to \(\frac{7}{4}\):
\[ \frac{7}{4} + \frac{1}{4} = \frac{8}{4} = 2 \]

4. **Conclusion**:
- The next term in the series is \(2\).

### Final Answer:
The next term in the series is \(2\).