Direction : A series is given with one term missing. Choose the correct alternative from the given ones:
2, 3, 5, 9, 17, ? / निर्देश : निम्नलिखित प्रत्येक प्रश्न में एक अनुक्रम दिया है, जिसमें एक पद लुप्त है। दिये गये विकल्पों में से सही विकल्प चुनिये जो अनुक्रम को पूरा करे :
`2, 3, 5, 9, 17, ?`

Options

A. 31
B. 32
C. 33
D. 34

Explanation

To find the missing term in the series 2, 3, 5, 9, 17, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the differences between consecutive terms
Let's find the differences between each pair of consecutive terms in the series:

- 3 - 2 = 1
- 5 - 3 = 2
- 9 - 5 = 4
- 17 - 9 = 8

So, the differences are: 1, 2, 4, 8.

### Step 2: Observe the pattern in the differences
Now, let's analyze the differences we found:

- The differences are: 1, 2, 4, 8.
- We can see that each difference is double the previous one (1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8).

### Step 3: Predict the next difference
Following the pattern, the next difference should be:

- 8 * 2 = 16.

### Step 4: Add the next difference to the last term in the series
Now, we will add this next difference (16) to the last known term in the series (17):

- 17 + 16 = 33.

### Conclusion
Thus, the missing term in the series is **33**.

### Final Answer
The missing term is **33**.

---