Select the missing number from the given series.
0, 6, 20, 42, ?

Options

A. 72
B. 65
C. 62
D. 75

Answer

To find the missing number in the series 0, 6, 20, 42, ?, we can analyze the pattern in the sequence.

1. **Identify the pattern**:
We observe the given numbers:
- 0
- 6
- 20
- 42

2. **Express each number in terms of a formula**:
Let's see if we can express these numbers in a formula.
- The first term (0) can be expressed as \(0 \times 1\).
- The second term (6) can be expressed as \(2 \times 3\).
- The third term (20) can be expressed as \(4 \times 5\).
- The fourth term (42) can be expressed as \(6 \times 7\).

3. **Recognize the pattern**:
From the above, we can see a pattern:
- The nth term can be represented as \(n \times (n + 1)\), where n is an even number starting from 0.
- Specifically:
- For the 1st term: \(0 \times 1 = 0\)
- For the 2nd term: \(2 \times 3 = 6\)
- For the 3rd term: \(4 \times 5 = 20\)
- For the 4th term: \(6 \times 7 = 42\)

4. **Calculate the next term**:
Following the pattern, the next term would be:
- For the 5th term: \(8 \times 9 = 72\)

5. **Conclusion**:
Therefore, the missing number in the series is **72**.