Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 3 such that the first three numbers are as listed in the question followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
For example,
You want the next number to be 1? Then U(n) = (-20n^3 + 123n^2 - 214n + 171)/3
You want the next number to be 2? Then U(n) = (-13n^3 + 80n^2 - 139n + 112)/2You want the next number to be 11? Then U(n) = -7n^3 + 40n^2 - 70n + 56
You want the next number to be 101? Then U(n) = 10n^3 - 59n^2 + 112n - 43
The next number in the sequence would be 25.
The sequence of differences between consecutive numbers is 9, 1, -20, 9, 1. If this continues then the next difference is -20 and therefore the seventh number is -5. (15 - 20).
The sequence appears to be decreasing with varying intervals: 50 to 33 (17), 33 to 25 (8), 25 to 20 (5), 20 to 17 (3), 17 to 14 (3), 14 to 13 (1), and 13 to 11 (2). The differences between the numbers suggest that the next number decreases by 1 from 11, resulting in 10. Therefore, the next number in the sequence is 10.
243
It is obvious that 7 is added to get the next number from the previous one.
25 is the next number that appears in that sequence.
The next number in the sequence would be 25.
The rule is 5 10 15 20 25 30 .... etc and accordingly the next number in the sequence will be 106
The sequence of differences between consecutive numbers is 9, 1, -20, 9, 1. If this continues then the next difference is -20 and therefore the seventh number is -5. (15 - 20).
The sequence of differences between consecutive numbers is 9, 1, -20, 9, 1. If this continues then the next difference is -20 and therefore the seventh number is -5. (15 - 20).
The sequence appears to be decreasing with varying intervals: 50 to 33 (17), 33 to 25 (8), 25 to 20 (5), 20 to 17 (3), 17 to 14 (3), 14 to 13 (1), and 13 to 11 (2). The differences between the numbers suggest that the next number decreases by 1 from 11, resulting in 10. Therefore, the next number in the sequence is 10.
121.
243
It is obvious that 7 is added to get the next number from the previous one.
Each is half of the previous number, so 6.25 will be next.
35
To find the next number in the sequence 4, 11, 25, 53, we can observe the differences between consecutive terms: 11 - 4 = 7, 25 - 11 = 14, and 53 - 25 = 28. The differences (7, 14, 28) double each time, suggesting the next difference should be 56. Adding this to the last number, 53 + 56, we get 109 as the next number in the sequence.