A series is given with one term missing. Choose the correct alternative from the given ones :
2, 7, 16, ?, 46,67
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, 7, 16, ?, 46,67

Options

A. 26
B. 27
C. 29
D. 31

Explanation

To find the missing term in the series 2, 7, 16, ?, 46, 67, we can follow these steps:

### Step 1: Identify the given series
The series is: 2, 7, 16, ?, 46, 67.

### Step 2: Calculate the differences between consecutive terms
Let's calculate the differences between the known terms:
- Difference between 2 and 7: \(7 - 2 = 5\)
- Difference between 7 and 16: \(16 - 7 = 9\)
- Difference between 16 and the missing term: We will denote this difference as \(x\).
- Difference between the missing term and 46: \(46 - ?\)
- Difference between 46 and 67: \(67 - 46 = 21\)

So far, we have:
- 2 to 7: 5
- 7 to 16: 9
- 16 to ?: \(x\)
- ? to 46: \(46 - ?\)
- 46 to 67: 21

### Step 3: Look for a pattern in the differences
Now, let's analyze the differences we have:
- The difference from 2 to 7 is 5.
- The difference from 7 to 16 is 9.
- The difference from 46 to 67 is 21.

### Step 4: Find the pattern in the differences
We can see that the differences are increasing:
- From 5 to 9, the increase is \(9 - 5 = 4\).
- From 9 to \(x\), we can assume the increase continues by 4, so \(x = 9 + 4 = 13\).
- From \(x\) to 21, we can check if the pattern holds. If \(x = 13\), then the difference from 16 to the missing term is 13.

### Step 5: Calculate the missing term
Now we can find the missing term:
- The missing term = 16 + 13 = 29.

### Step 6: Verify the next difference
Now, let's check the difference from the missing term (29) to 46:
- \(46 - 29 = 17\), which continues the pattern of increasing differences (from 13 to 17, the increase is 4).

### Conclusion
Thus, the missing term in the series is **29**.