What will come in the place of question mark (?) in the following series questions?
18,25,30,?,42,49

Options

A. A)37
B. B)35
C. C)39
D. D)41

Answer

To find the missing term in the series 18, 25, 30, ?, 42, 49, we will analyze the differences between the consecutive terms.

### Step-by-Step Solution:

1. **Identify the given series**:
The series is: 18, 25, 30, ?, 42, 49.

2. **Calculate the differences between consecutive terms**:
- From 18 to 25:
\[ 25 - 18 = 7 \]
- From 25 to 30:
\[ 30 - 25 = 5 \]
- From 30 to ?:
Let's denote the missing term as \( K \).
- From \( K \) to 42:
\[ 42 - K \]
- From 42 to 49:
\[ 49 - 42 = 7 \]

3. **Establish a pattern in the differences**:
The differences we have so far are:
- 7 (from 18 to 25)
- 5 (from 25 to 30)
- (unknown difference from 30 to \( K \))
- (unknown difference from \( K \) to 42)
- 7 (from 42 to 49)

Observing the differences, we can see a pattern emerging:
- The differences seem to alternate between 7 and 5.

4. **Determine the missing difference**:
If we follow the established pattern:
- After 30, we expect a difference of 7 (since the last known difference before 42 is 7).
- Therefore, we can calculate \( K \) as:
\[ K = 30 + 7 = 37 \]

5. **Verify the pattern**:
Now, let's check if this value fits the pattern:
- From 30 to 37:
\[ 37 - 30 = 7 \]
- From 37 to 42:
\[ 42 - 37 = 5 \]
- From 42 to 49:
\[ 49 - 42 = 7 \]
This confirms the alternating pattern of differences: 7, 5, 7, 5, 7.

6. **Conclusion**:
The missing term \( K \) in the series is:
\[ \boxed{37} \]