The missing number in the series 5, 16, 51, 158 is 481.
Understanding the Pattern
The given series is: 5, 16, 51, 158, and we need to determine the next number. By analyzing the differences and multiplication patterns, we can find the following pattern:
| Position | Number | Calculation |
|---|---|---|
| 1 | 5 | |
| 2 | 16 | (5 * 3) + 1 |
| 3 | 51 | (16 * 3) + 3 |
| 4 | 158 | (51 * 3) + 5 |
| 5 | 481 | (158 * 3) + 7 |
Detailed Explanation:
The series is not a simple arithmetic or geometric progression. The pattern involves multiplying the previous number by 3 and then adding an odd number which increases by 2 each time. This can be shown as follows:
- 5 is our starting point.
- 16 is calculated as (5 * 3) + 1.
- 51 is calculated as (16 * 3) + 3.
- 158 is calculated as (51 * 3) + 5.
- Following this pattern, the next number is calculated as (158 * 3) + 7.
Therefore, the missing number in the series is: (158 * 3) + 7 = 474 + 7 = 481.
Summary
- The series follows the rule:
Number_n = (Number_n-1 * 3) + (2n - 1), where n is the position of the number in the series, starting from 1 for the second number. - Based on the reference provided, the next term in the series is 481.
