What should come in place of question mark (?) in the following number series?
5 ? 15 75 525 4725 51975

Options

A. 5
B. 10
C. 8
D. 6

Answer

To find the missing number in the series: 5, ?, 15, 75, 525, 4725, 51975, we can analyze the pattern in the series.

1. **Identify the pattern**:
- The numbers after the missing number are: 15, 75, 525, 4725, 51975.
- Let's look at the relationship between these numbers.

2. **Calculate the ratios**:
- 15 to 75: \( 15 \times 5 = 75 \)
- 75 to 525: \( 75 \times 7 = 525 \)
- 525 to 4725: \( 525 \times 9 = 4725 \)
- 4725 to 51975: \( 4725 \times 11 = 51975 \)

Here, we can see that each number is multiplied by an increasing odd number: 5, 7, 9, and 11.

3. **Establish the relationship for the missing number**:
- We can see that the number before 15 (the missing number) must be multiplied by 3 to yield 15.
- Therefore, if we denote the missing number as \( x \), we have:
\[ x \times 3 = 15 \]

4. **Solve for the missing number**:
- Rearranging the equation gives:
\[ x = \frac{15}{3} = 5 \]

5. **Conclusion**:
- The missing number in the series is 5.

Thus, the answer is 5.