A series is given with one term missing. Choose the correct alternative from the give ones:
14,27,52,101,198?
निम्नलिखित प्रत्येक प्रश्न में एक अनुक्रम दिया है जिसमे एक पद लुप्त है। दिये गये विकल्पों में से सही विकल्प चुनिए जो अनुक्रम को पूरा करे:
14,27,52,101,198?

Options

A. 381
B. 395
C. 391
D. 394

Explanation

To solve the given series: 14, 27, 52, 101, 198, we need to identify the pattern that governs the sequence.

### Step-by-Step Solution:

1. **Identify the first term and the operation applied:**
- The first term is 14.
- The operation appears to be: Multiply by 2 and then subtract a certain number.
- Let's check the first term:
- \( 14 \times 2 - 1 = 28 - 1 = 27 \)

2. **Check the second term:**
- Now, take the second term (27):
- \( 27 \times 2 - 2 = 54 - 2 = 52 \)

3. **Check the third term:**
- Now, take the third term (52):
- \( 52 \times 2 - 3 = 104 - 3 = 101 \)

4. **Check the fourth term:**
- Now, take the fourth term (101):
- \( 101 \times 2 - 4 = 202 - 4 = 198 \)

5. **Identify the pattern:**
- The pattern we observe is:
- Multiply by 2 and subtract increasing integers:
- First term: -1
- Second term: -2
- Third term: -3
- Fourth term: -4

6. **Apply the pattern to find the next term:**
- For the fifth term (198):
- \( 198 \times 2 - 5 = 396 - 5 = 391 \)

7. **Conclusion:**
- The next term in the series is 391.

### Final Answer:
The missing term in the series is **391**.