a = 11 (242) 121,
b = 14 (392) 196 ,
C = 13 (?) 169

Options

A. 182
B. 338
C. 2197
D. 28224

Explanation

To solve the problem, we need to identify the pattern in the given equations for \( a \) and \( b \), and then apply the same pattern to find the missing value for \( c \).

### Step-by-Step Solution:

1. **Identify the Pattern in \( a \)**:
- Given: \( a = 11 (242) 121 \)
- We notice that \( 11^2 = 121 \).
- The middle term \( 242 \) can be derived by adding \( 121 \) to itself: \( 121 + 121 = 242 \).
- Thus, the pattern for \( a \) is:
\[ a = x \quad (2x^2) \quad x^2 \]
- Where \( x = 11 \).

2. **Identify the Pattern in \( b \)**:
- Given: \( b = 14 (392) 196 \)
- Here, \( 14^2 = 196 \).
- The middle term \( 392 \) is obtained by adding \( 196 \) to itself: \( 196 + 196 = 392 \).
- The pattern for \( b \) is:
\[ b = x \quad (2x^2) \quad x^2 \]
- Where \( x = 14 \).

3. **Apply the Pattern to \( c \)**:
- Given: \( c = 13 (?) 169 \)
- We first calculate \( 13^2 = 169 \).
- To find the middle term, we add \( 169 \) to itself: \( 169 + 169 = 338 \).
- Therefore, we can express \( c \) as:
\[ c = 13 \quad (338) \quad 169 \]

4. **Final Result**:
- The missing term in \( c \) is \( 338 \).
- Thus, \( c = 13 (338) 169 \).

### Conclusion:
The value for \( c \) is \( 338 \).