What will come in place of question mark(?) in the given number series?
12 181 302 383 ? 457

Options

A. 395
B. 432
C. 386
D. 447

Answer

To find the missing number in the series: 12, 181, 302, 383, ?, 457, we will analyze the differences between the consecutive numbers.

1. **Calculate the differences between the numbers:**
- Difference between 181 and 12:
\[ 181 - 12 = 169 \]
- Difference between 302 and 181:
\[ 302 - 181 = 121 \]
- Difference between 383 and 302:
\[ 383 - 302 = 81 \]

2. **List the differences:**
- The differences we have calculated are:
- 169
- 121
- 81

3. **Identify the pattern in the differences:**
- The differences are:
- \( 13^2 = 169 \)
- \( 11^2 = 121 \)
- \( 9^2 = 81 \)
- We can see that the differences are squares of odd numbers decreasing by 2:
- Next difference should be \( 7^2 = 49 \).

4. **Calculate the next number in the series:**
- Add the next difference (49) to the last known number (383):
\[ 383 + 49 = 432 \]

5. **Verify the next difference:**
- The next number after the missing number should be 457. Calculate the difference:
\[ 457 - 432 = 25 \]
- \( 5^2 = 25 \), which confirms our pattern.

6. **Conclusion:**
- The missing number in the series is:
\[ \text{Missing number} = 432 \]

Thus, the answer is 432.