What will come in the place of question mark (?) in the following number sereis:
`0," "6", "24," "60," "?," "210`

Options

A. A)130
B. B)170
C. C)90
D. D)120

Answer

To find the missing term in the series: 0, 6, 24, 60, ?, 210, we can analyze the differences between the terms and look for a pattern.

### Step-by-Step Solution:

1. **Write down the series:**
The series is: 0, 6, 24, 60, ?, 210.

2. **Calculate the first differences:**
- From 0 to 6: \( 6 - 0 = 6 \)
- From 6 to 24: \( 24 - 6 = 18 \)
- From 24 to 60: \( 60 - 24 = 36 \)
- From 60 to ?: Let’s denote this difference as \( K \).
- From ? to 210: \( 210 - ? \)

So, the first differences are: 6, 18, 36, K, (210 - ?).

3. **Calculate the second differences:**
- From 6 to 18: \( 18 - 6 = 12 \)
- From 18 to 36: \( 36 - 18 = 18 \)
- From 36 to K: \( K - 36 \)
- From K to (210 - ?): \( (210 - ?) - K \)

The second differences are: 12, 18, (K - 36), ((210 - ?) - K).

4. **Identify the pattern in the second differences:**
The second differences seem to be increasing. The difference from 12 to 18 is 6. If we continue this pattern, the next difference should be \( 18 + 6 = 24 \).

5. **Set up the equation:**
From the second difference, we have:
\[ K - 36 = 24 \]
Solving for \( K \):
\[ K = 24 + 36 = 60 \]

6. **Calculate the next first difference:**
Now, we know that \( K = 60 \). We can find the difference from 60 to the next term:
\[ (210 - ?) - 60 = 24 \]
Solving for \( 210 - ? \):
\[ 210 - ? = 24 + 60 = 84 \]
Therefore, \( ? = 210 - 84 = 126 \).

7. **Final answer:**
The missing term in the series is 120.

### Conclusion:
The missing term in the series is **120**.