Find out the missing term in the series 0,6,24,60,120,`"……….."`.

Answer

To find the missing term in the series 0, 6, 24, 60, 120, "………..", we can analyze the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The given series is:
- 0
- 6
- 24
- 60
- 120

2. **Express Each Term**:
Let's express each term in the series using a formula. We can observe that:
- The first term (0) can be expressed as \(0 \times 1 \times 2\).
- The second term (6) can be expressed as \(1 \times 2 \times 3\).
- The third term (24) can be expressed as \(2 \times 3 \times 4\).
- The fourth term (60) can be expressed as \(3 \times 4 \times 5\).
- The fifth term (120) can be expressed as \(4 \times 5 \times 6\).

3. **Generalize the Formula**:
From the above observations, we can see that the nth term can be expressed as:
\[ T_n = (n-1) \times n \times (n+1) \]
where \(n\) starts from 1.

4. **Calculate the Missing Term**:
To find the missing term, we need to calculate the 6th term:
\[ T_6 = (6-1) \times 6 \times (6+1) = 5 \times 6 \times 7 \]

5. **Perform the Calculation**:
Now, calculate \(5 \times 6 \times 7\):
\[ 5 \times 6 = 30 \]
\[ 30 \times 7 = 210 \]

6. **Conclusion**:
Therefore, the missing term in the series is **210**.