Select the option that can replace the question mark (?) and complete the given series.
18, 21, 26, 33, 42, ?, ?

Options

A. 65,83
B. 52,64
C. 53,66
D. 65,74

Answer

To solve the series 18, 21, 26, 33, 42, ?, ?, we will analyze the differences between the consecutive terms and identify a pattern.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 18, 21, 26, 33, 42.

2. **Calculate the differences between consecutive terms**:
- Difference between 21 and 18:
\[ 21 - 18 = 3 \]
- Difference between 26 and 21:
\[ 26 - 21 = 5 \]
- Difference between 33 and 26:
\[ 33 - 26 = 7 \]
- Difference between 42 and 33:
\[ 42 - 33 = 9 \]

3. **List the differences**: The differences are 3, 5, 7, and 9.

4. **Identify the pattern in the differences**: The differences are increasing by 2 each time:
- 3 (1st difference)
- 5 (2nd difference)
- 7 (3rd difference)
- 9 (4th difference)

5. **Predict the next differences**: Following the pattern, the next differences should be:
- 11 (5th difference)
- 13 (6th difference)

6. **Calculate the next terms in the series**:
- To find the 5th term (after 42), we add the next difference (11):
\[ 42 + 11 = 53 \]
- To find the 6th term (after 53), we add the next difference (13):
\[ 53 + 13 = 66 \]

7. **Final series**: The complete series is 18, 21, 26, 33, 42, 53, 66.

### Conclusion:
The two missing numbers in the series are **53 and 66**.