Complete the number series by choosing the missing terms from the options.
32, 64, 256, 1536, ? ,122880, 1474560

Options

A. 122860
B. 12268
C. 12285
D. 12288

Answer

To solve the number series: 32, 64, 256, 1536, ?, 122880, 1474560, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- Let's examine the relationship between the consecutive numbers in the series.
- The first number is 32, the second is 64. We can see that:
- \( 64 = 32 \times 2 \)

2. **Continue the Pattern**:
- Now, moving to the next number:
- \( 256 = 64 \times 4 \)
- The multiplication factor has changed from 2 to 4.

3. **Next Step**:
- Now, let's check the next number:
- \( 1536 = 256 \times 6 \)
- The multiplication factor has increased to 6.

4. **Finding the Missing Term**:
- Following the pattern, the next multiplication factor should be 8:
- \( ? = 1536 \times 8 \)
- Calculating this gives:
- \( ? = 1536 \times 8 = 12288 \)

5. **Verify the Next Number**:
- Now, let's check the next number in the series:
- \( 122880 = 12288 \times 10 \)
- This confirms our missing term is correct.

6. **Final Confirmation**:
- The last number in the series is:
- \( 1474560 = 122880 \times 12 \)
- This maintains the pattern of increasing multiplication factors (2, 4, 6, 8, 10, 12).

### Conclusion:
The missing term in the series is **12288**.