What will come in place of (?) in the following number series problems?
`5," "30," "150," "600," "?`

Options

A. A)1200
B. B)1500
C. C)2400
D. D)1800

Answer

To solve the number series problem: `5, ?, 30, 150, 600, ?`, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Terms**:
The given series is:
- First term (T1) = 5
- Second term (T2) = ?
- Third term (T3) = 30
- Fourth term (T4) = 150
- Fifth term (T5) = 600
- Sixth term (T6) = ?

2. **Finding the Pattern**:
Let's examine how each term relates to the previous one:
- From T1 to T3:
- T2 = T1 × 6 = 5 × 6 = 30
- From T3 to T4:
- T4 = T3 × 5 = 30 × 5 = 150
- From T4 to T5:
- T5 = T4 × 4 = 150 × 4 = 600

We can see that each term is obtained by multiplying the previous term by a decreasing integer (6, 5, 4).

3. **Continuing the Pattern**:
Following the established pattern:
- To find T6, we multiply T5 by 3:
- T6 = T5 × 3 = 600 × 3 = 1800

4. **Conclusion**:
The missing term (T2) can be calculated as follows:
- T2 = T1 × 6 = 5 × 6 = 30 (already known)
- Therefore, the fifth term (T5) is 600 and the sixth term (T6) is 1800.

Thus, the answer to the question is **1800**.