Which number will fit in '?' place in the following series ?
2, ?, 12, 20, 30, 42
A. 2 B. 4 C. 6 D. 8

Options

A. D
B. C
C. A
D. B

Answer

To find the missing number in the series 2, ?, 12, 20, 30, 42, we will analyze the differences between the consecutive numbers.

1. **Identify the given series**:
- The series is: 2, ?, 12, 20, 30, 42.

2. **Calculate the differences between the known numbers**:
- The difference between 12 and 20 is:
\[ 20 - 12 = 8 \]
- The difference between 20 and 30 is:
\[ 30 - 20 = 10 \]
- The difference between 30 and 42 is:
\[ 42 - 30 = 12 \]

3. **Observe the pattern in the differences**:
- The differences we found are: 8, 10, and 12.
- We can see that the differences are increasing by 2 each time.

4. **Determine the difference before 12**:
- Since the differences are increasing by 2, the difference before 12 should be:
\[ 8 - 2 = 6 \]

5. **Calculate the missing number**:
- If the difference between the missing number (let's call it x) and 12 is 6, we can set up the equation:
\[ 12 - x = 6 \]
- Solving for x gives:
\[ x = 12 - 6 = 6 \]

6. **Check the difference between 2 and the missing number**:
- Now we check the difference between 2 and the missing number (6):
\[ 6 - 2 = 4 \]
- The difference between 2 and 6 is 4.

7. **Verify the entire series**:
- Now we can write the complete series as: 2, 6, 12, 20, 30, 42.
- The differences are:
- 6 - 2 = 4
- 12 - 6 = 6
- 20 - 12 = 8
- 30 - 20 = 10
- 42 - 30 = 12
- The differences are indeed increasing by 2.

Thus, the missing number is **6**.

### Final Answer:
The number that fits in the '?' place is **6** (Option C).