What will come in the place of question mark (?) in the following number series? 3, 6, 18, ?, 630, 6930
90
Number Series Pattern Analysis
The question asks us to find the missing number in the given number series: 3, 6, 18, ?, 630, 6930.
We need to identify the logical relationship or pattern between the consecutive numbers in the series to determine the value that should replace the question mark.
Finding the Relationship Between Terms
Let's examine the relationship between the first few terms:
- From 3 to 6: The number is multiplied by 2. (
3 \times 2 = 6
) - From 6 to 18: The number is multiplied by 3. (
6 \times 3 = 18
)
We observe that the multiplier is increasing. Let's hypothesize that the multipliers are sequential prime numbers.
Step-by-Step Solution Using Prime Multipliers
The sequence of multipliers starts with 2, then 3. The next prime numbers are 5, 7, 11, and so on. Let's test this hypothesis:
| Term | Multiplier | Next Term | Calculation |
| 3 | 2 (1st Prime) |
6 | 3 \times 2 = 6 |
| 6 | 3 (2nd Prime) |
18 | 6 \times 3 = 18 |
| 18 | 5 (3rd Prime) |
? | 18 \times 5 = 90 |
| ? (Result is 90) | 7 (4th Prime) |
630 | 90 \times 7 = 630 |
| 630 | 11 (5th Prime) |
6930 | 630 \times 11 = 6930 |
The pattern holds true. The series is generated by multiplying the current term by consecutive prime numbers starting from 2.
Identifying the Missing Number
Based on the identified pattern of multiplying by consecutive prime numbers (2, 3, 5, 7, 11), the missing number is calculated as follows:
- The term before the question mark is 18.
- The multiplier needed is the next prime number after 3, which is 5.
- Calculation:
18 \times 5 = 90
To confirm, the next step should be multiplying 90 by the next prime number, 7:
- Calculation:
90 \times 7 = 630
This matches the subsequent term in the series. Therefore, the missing number is 90.
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