What will come in place of question mark (?) in the following series questions?
12,14,17,22,29,?

Options

A. A)41
B. B)40
C. C)38
D. D)45

Answer

To find the missing term in the series 12, 14, 17, 22, 29, ?, we will analyze the differences between consecutive terms and identify a pattern.

### Step-by-Step Solution:

1. **Identify the Given Series:**
The series is: 12, 14, 17, 22, 29, ?

2. **Calculate the Differences Between Consecutive Terms:**
- Difference between 14 and 12:
\( 14 - 12 = 2 \)
- Difference between 17 and 14:
\( 17 - 14 = 3 \)
- Difference between 22 and 17:
\( 22 - 17 = 5 \)
- Difference between 29 and 22:
\( 29 - 22 = 7 \)

So, the differences are: 2, 3, 5, 7.

3. **Identify the Pattern in the Differences:**
The differences we calculated (2, 3, 5, 7) are all prime numbers. The sequence of prime numbers starts with 2, 3, 5, 7, and the next prime number after 7 is 11.

4. **Add the Next Prime Number to the Last Term:**
To find the missing term, we will add the next prime number (11) to the last term in the series (29):
\[ 29 + 11 = 40 \]

5. **Conclusion:**
The missing term in the series is 40.

### Final Answer:
The missing term is **40**.

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