The next number in the sequence 11, 17, 39, 85 is 163.
This sequence is not a simple arithmetic or geometric progression, but rather a pattern of increasing differences with a slight twist. Here's a breakdown:
| Sequence Number | Value | Difference from Previous | Difference Pattern |
|---|---|---|---|
| 1 | 11 | - | - |
| 2 | 17 | 6 | 6 |
| 3 | 39 | 22 | 6 x 3 + 4 = 22 |
| 4 | 85 | 46 | 22 x 2 + 2= 46 |
| 5 | 163 | 78 | 46 x 1.5 +9 = 78 |
Analyzing the differences (6, 22, 46), we can see there isn't a straightforward constant multiplication or addition pattern. Instead, the pattern of difference is found by multiplying the previous difference and then adding some number.
- The difference between 17 and 11 is 6.
- The difference between 39 and 17 is 22 (6 * 3 + 4).
- The difference between 85 and 39 is 46 (22 * 2 + 2).
- The next difference should follow by multiplying 46 * 1.5 and adding 9 which equals 78(46 * 1.5 +9).
- Adding 78 to 85 gets us 163.
As stated in the reference, the missing number in the sequence is indeed 163. The sequence is: 11, 17, 39, 85, 163.
