What will come in place of the question mark (?) in the following number series?
`14" "43.5" " 264" "?" "76188`

Options

A. A)3168
B. B)3176
C. C)1587
D. D)None of these

Answer

To find the missing term in the series `14, 43.5, 264, ?, 76188`, we will analyze the pattern followed by the terms.

### Step-by-Step Solution:

1. **Identify the first term**: The first term is \( 14 \).

2. **Calculate the second term**:
- We add \( 0.5 \) to the first term:
\[ 14 + 0.5 = 14.5 \]
- Then, we multiply this result by \( 3 \):
\[ 14.5 \times 3 = 43.5 \]
- Thus, the second term is \( 43.5 \).

3. **Calculate the third term**:
- We take the second term \( 43.5 \) and add \( 0.5 \):
\[ 43.5 + 0.5 = 44 \]
- Next, we multiply this result by \( 6 \):
\[ 44 \times 6 = 264 \]
- Therefore, the third term is \( 264 \).

4. **Calculate the fourth term**:
- Now, we take the third term \( 264 \) and add \( 0.5 \):
\[ 264 + 0.5 = 264.5 \]
- We then multiply this result by \( 12 \):
\[ 264.5 \times 12 = 3174 \]
- Hence, the fourth term is \( 3174 \).

5. **Calculate the fifth term**:
- Next, we take the fourth term \( 3174 \) and add \( 0.5 \):
\[ 3174 + 0.5 = 3174.5 \]
- Finally, we multiply this result by \( 12 \):
\[ 3174.5 \times 12 = 76188 \]
- This confirms that the fifth term is \( 76188 \).

### Conclusion:
The missing term in the series is \( 3174 \).