Finding the Missing Number in the Series

The question asks us to identify the correct number to replace the question mark (?) in the given number series. The series provided is: 6, 6, 18, 90, 630, ?

Analyzing the Series Pattern

To find the missing number, we first need to understand the pattern governing the series. Let's examine the relationship between consecutive terms:

• The first term is 6.
• The second term is 6. The relationship between the first and second term is $6 \times 1 = 6$.
• The third term is 18. The relationship between the second and third term is $6 \times 3 = 18$.
• The fourth term is 90. The relationship between the third and fourth term is $18 \times 5 = 90$.
• The fifth term is 630. The relationship between the fourth and fifth term is $90 \times 7 = 630$.

By observing these steps, we can see a clear pattern: each term is obtained by multiplying the previous term by consecutive odd numbers, starting from 1. The sequence of multipliers is 1, 3, 5, 7.

Calculating the Next Number

Following the established pattern, the next multiplier should be the next odd number after 7, which is 9.

To find the missing number (the sixth term in the series), we need to multiply the last given term (630) by the next multiplier (9).

The calculation is as follows:

$$630 \times 9$$

Let's perform the multiplication:

$$630 \times 9 = 5670$$

So, the number that should replace the question mark is 5670.

Selecting the Correct Option

We need to choose the option that matches our calculated value.

• Option 1: 8500
• Option 2: 1260
• Option 3: 4250
• Option 4: 5670
• Option 5: (No value provided)

Our calculated result is 5670, which corresponds to Option 4.