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Given any number it is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.
The simplest polynomial solution, of order 4, is
Un = (-n4 + 10n3 - 11n2 - 142n + 456)/24 for n = 1, 2, 3, ...
and accordingly, the next in the sequence is U6 = 3.
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What number is next in this sequence 3 4 6 9 13?
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.
What is the next number in the sequence 5-7-13-31?
The next number in the sequence 5-7-13-31 is 69.
What is the rule for this sequence 3 4 6 9 13 18?
The rule for this sequence appears to be adding consecutive prime numbers. The sequence starts with 3, then adds the next prime number 2 to get 4. It then adds 3 (the next prime number) to 4 to get 7, then 5 to 7 to get 12, and so on. Each number in the sequence is the sum of the previous number and the next prime number in order.
What is the next term in the sequence -13-9-5-1?
3
What is the next term in sequence in 1-4-8-13?
19. Add 3, then add 4, then add 5, then add 6,etc.
