Any number can be the next number. It is easy to find a rule based on a polynomial of order 4 such that the first four 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.
The simplest solution, based on a polynomial of order 3, is
T(n) = (-19n^3 + 143n^2 - 331n + 246)/3 where n = 1, 2, 3, ...
and accordingly, the next number is 53.
15
The next number in the sequence 5-7-13-31 is 69.
The sequence alternates between a number and that number plus one. After 2 comes 3, after 3 comes 12, after 12 comes 13, after 13 comes 52, and after 52 comes 53. Following this pattern, the next number after 53 would be 212, as it follows 52 multiplied by 4 (the previous non-incrementing number). Therefore, the next number in the sequence is 212.
The nest number in the sequence is 18. Note that the difference between each number and the next number in the sequence follows the simple sequence of 1,2,3,4. Obviously the next in the sequence of increases is 5, so 13+5=18.
The sequence 0112358 represents the Fibonacci sequence, where each number is the sum of the two preceding ones. The next number in this sequence is 13, as it is the sum of the last two numbers, 5 and 8. Thus, the next number is 13.
20
11
11
15
11.
The next number in the sequence 5-7-13-31 is 69.
21
22
17?
15
The nest number in the sequence is 18. Note that the difference between each number and the next number in the sequence follows the simple sequence of 1,2,3,4. Obviously the next in the sequence of increases is 5, so 13+5=18.
The sequence 0112358 represents the Fibonacci sequence, where each number is the sum of the two preceding ones. The next number in this sequence is 13, as it is the sum of the last two numbers, 5 and 8. Thus, the next number is 13.