Find the missing number:
2, 6, 14, 26, ........, 62

Options

A. 52
B. 54
C. 44
D. 42

Explanation

To find the missing number in the sequence: 2, 6, 14, 26, __, 62, we will analyze the differences between the numbers step by step.

### Step 1: Write down the sequence
The sequence we have is:
2, 6, 14, 26, __, 62

### Step 2: Calculate the differences between consecutive terms
- The difference between 6 and 2 is:
\( 6 - 2 = 4 \)

- The difference between 14 and 6 is:
\( 14 - 6 = 8 \)

- The difference between 26 and 14 is:
\( 26 - 14 = 12 \)

### Step 3: Identify the pattern in the differences
Now we have the differences:
- From 2 to 6: 4
- From 6 to 14: 8
- From 14 to 26: 12

We can see that the differences themselves are increasing:
- The difference from 4 to 8 is \( 8 - 4 = 4 \)
- The difference from 8 to 12 is \( 12 - 8 = 4 \)

This indicates that the differences are increasing by 4 each time.

### Step 4: Calculate the next difference
Following the pattern, the next difference after 12 should be:
\( 12 + 4 = 16 \)

### Step 5: Find the missing number
Now, we add this difference to the last known number in the sequence (26):
\( 26 + 16 = 42 \)

### Step 6: Verify the next difference
To ensure our answer is correct, we need to check the difference from 42 to 62:
- The difference should be:
\( 62 - 42 = 20 \)

### Conclusion
Since the differences follow the established pattern (4, 8, 12, 16, 20), the missing number in the sequence is:
**42**